I’m trying to find the absolute Max and min, I can’t figure out how to do the derivative, thanks

Im Trying To Find The Absolute Max And Min, I Cant Figure Out How To Do The Derivative, Thanks

Answers

Answer 1

Step-by-step explanation:

Step 1: Take the First Derivative This means only differentiate once.

Disclaimer: Since absolute value only take positve outputs and quadratics only take positve outputs, we can get rid of the absolute value signs so we now have

[tex]e {}^{ {x}^{2} - 1 } [/tex]

We have the function x^2-1 composed into the function e^x.

So we use chain rule

Which states the derivative of a function composed is the

derivative of the main function times the derivative of the inside function.

So the derivative of the main function is

[tex] \frac{d}{dx} (e {}^{x} ) = e {}^{x} [/tex]

Then we replace x with x^2-1

[tex]e {}^{ {x}^{2} - 1} [/tex]

Then we take the derivative of the second function which is 2x so qe multiply them

[tex]e { }^{ {x}^{2} - 1 } 2x[/tex]

Step 2: Set the equation equal to zero.

[tex]e {}^{x {}^{2} - 1} 2x = 0[/tex]

Since e doesn't reach zero. We can just set 2x=0.

[tex]2x = 0 = x = 0[/tex]

So the critical point is 0.

Since e^x will never reach zero

Since 0 is the only critical point, this where the max or min will occur at.

Next we pick any numbergreater than zero, and plug them in the derivative function which gives us a positve number.

Any pick less than zero will give us a negative number.

Since the function is decreasing then increasing, we have a minimum.

Since 0 is the only critical point, we have a absolute minimum at 0.

To find the y coordinate, plug 0 in the orginal function.

Which gives us

[tex]e {}^{ {0}^{2} - 1 } = e {}^{ - 1} = \frac{1}{e} [/tex]

So the minimum occurs at

(0,1/e).


Related Questions

What is the value of x?

Answers

Answer:

lj= lk din 30 give lj= 4✓2

and ml=x= lj cos 45

on solving x= 4✓2 cos45=4

tim drives at an average of 80km per hour for 3 hours 45 minutes. work out how many kilometres tim drives

Answers

Tim covered 21.333 kilometers

Kilometers, km covered is distance, d

d = speed / time

d = 80 / 3 hours 45 mins

Converting 45 mins to hours we have

1 hour = 60 minutes

? Hours = 45 minutes

? = 45 / 60 = 0.75

So time is 3.75 hours

d = 80 / 3.75

= 64 / 3

= 21.333km


hope it helps

Answer:

300 km

Step-by-step explanation:

Tim drives 80 km in 1 hour or 60 minutes

Tim drives in 1 minute = 80/60 km

so, tim drives in 3 hours 45 minutes ( 225 minutes)

[tex] \frac{80 \times 225}{60} [/tex]

= 300 km

5 divided by 62.55 need help asap due today and also i cant watch ads

Answers

the answer of 5/62.55 = 0.0799360512

Hi Guys ^^[tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex]​

Answers

Answer:

Hi shelp >//<

[tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][tex] [/tex][/tex]

Answer:

Hi shelp >//<

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Step-by-step explanation:

enebe eeeHAHAHA

What is the process of writing a number as a product of several factors

Answers

Answer:

Step-by-step explanation:

you need to write out all the numbers that contain the specific number in their times tables, for example. factors of 20 are 1, 20, 4, 5, and 2 because all these numbers have 20 in their times tables.

PLEASE HELP I WILL GIVE BRAINLIEST

Answers

Answer:

20 inches²

Step-by-step explanation:

perimeter = 8 + 3 + 5 + 4

= 20 inches²

PLEASE help me. Please. Which debates among historians over the effects of the Vietnam War did you discover in your research?

Answers

Answer:

The Domino Theory suggested that one nation becoming Communist makes it more likely that others will too. Without American involvement, the South would quickly have fallen to the North and the nation, united under Communism, would have joined the Communist bloc.                

Step-by-step explanation:

Katie ate dinner at a restaurant. The bill came to $77. If she left an 18% tip, how much was the tip?


Can someone pls help me?​

Answers

Answer:

$13.86

Step-by-step explanation:

Just multiply 77 by 18 percent as a decimal (.18) to get the answer, which is $13.86

Hopefully this helps- let me know if you have any questions!

Answer:the largest angle has a measure of _____degrees.

Answers

Answer:

depends mostly it'll b 180 degress

Step-by-step explanation:

How to write 12/4 as a whole number

Answers

Answer:

3

Step-by-step explanation:

12 Divided By 4 Is 3

And 3 Is A Whole Number

Your answer is 3

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!

What is an equation of the line that passes through (0, 4) and (2,8)?

Answers

Answer:

y=2x+4

Step-by-step explanation:

Hi there!

We are given the points (0, 4) and (2,8)

We want to write the equation of the line that passes through these two points

There are 3 ways to write the equation of the line, but the most common way is with slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

So, to use this way, we need to find the slope of the line

The slope can be calculated using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We are already given the points needed to find the slope, but let's label them to avoid any confusion

[tex]x_1=0\\y_1=4\\x_2=2\\y_2=8[/tex]

Now substitute these values into the formula.

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{8-4}{2-0}[/tex]

Subtract

m=[tex]\frac{4}{2}[/tex]

Divide

m=2

The slope of the line is 2

Here is the equation of the line so far:

y=2x+b

Now we need to find b

As stated before, b is the y intercept of the line, which is the point in where the line passes through the y axis; the value of x at this point is 0

One of the points we were given earlier is actually the y intercept of the line; that point is (0, 4) *notice how x=0 at this point

The value of b is the value of y at the y intercept; in this case, the value of b is 4

Substitute 4 as b into the equation

y=2x+4

Hope this helps!

See more on this topic here: https://brainly.com/question/27172025

An envelope is 8 centimeters wide, and it measures 17 centimeters along the diagonal. How tall is the envelope? centimeters​

Answers

Answer:

15cm

Step-by-step explanation:

√289-64√22515cm

© the envelope is 15cm rall.

Answer:

15cm

Step-by-step explanation:

√289-64

√225

15cm

1 Susie wants to make some hot cereal for breakfast. The directions say to use 3 cups
of water with 1 cup of cereal to make 4 servings. Susie only wants 1 serving.
a
How much cereal should she use?
b How much water should she use?

Answers

Using proportions to relate the amount of cups needed, it is found that she should use:

a) 0.25 cups of cereal.

b) 0.75 cups of water.

What is a proportion?

A proportion is a fraction of a total amount.

In this problem, for 4 servings, 3 cups of water and 1 cup of cereal is needed. One serving is one-fourth of the amount, hence:

Item a:

1/4 x 1 = 0.25 cups of cereal.

Item b:

1/4 x 3 = 3/4 = 0.75 cups of water.

More can be learned about proportions at https://brainly.com/question/24372153

Stedents are decorating a banner to hang in the school way. The banner is 9 1/2 feet long and 2 1/2 feet wide . What is the area of the border the students are decorating?
3 4/5square feet
12 square foot
24 square feet
23 3/4square feet

Answers

Answer:

it would be 12 square feet human

Step-by-step explanation:

9 1/2+2 1/2=12 so 12 square feet

Who is the father of maths???​

Answers

Answer: Archimedes

Step-by-step explanation:

Archimedes was considered the father of mathematics, simply because he made profound advancements in both science and math. His title is purely a nickname, and not because he actually created math.

Answer:

Archimedes is known as the Father Of Mathematics

Step-by-step explanation:

What is the area of this figure?​

Answers

[tex]a \: = \: square \: area \: + \: triangle \: area \: + \: rectangle \: area \: \\ [/tex]

[tex]a \: = (3 \times 3) + ( \frac{1}{2} \times 3 \times 11) + (3 \times 11) \\ [/tex]

[tex]a = 9 + \frac{33}{2} + 33 \\ [/tex]

[tex]a = 9 + 16.5 + 33[/tex]

[tex]a = 25.5 + 33[/tex]

[tex]a = 58.5 \: \: {ft}^{2} [/tex]

The sum of 9 times a number and 8 is 3

Answers

Answer: 9n+8=3

Step-by-step explanation:

Let's break this down

"sum" refers to addition so we must be adding 9 times a number and 8

So far we have "9 times a number + 8"

We can use the variable, n to represent "a number"

Now we have "9 times n +8"

"times" refers to multiplication, so we should multiply 9 and n

Now we have "9n+8"

"is 3" simply means that this will equal 3

So now we have the equation 9n+8=3

Need help with this geometric question ASAP, Thank you

Answers

Answer:

  a.  x = 9

  b.  GH = 30; GK = 20

Step-by-step explanation:

An angle bisector in a triangle divides the sides proportionally.

a.

In this triangle, that means ...

  (3x +3)/18 = (3x -7)/12

  2(3x +3) = 3(3x -7) . . . . . . . multiply by 36

  6x +6 = 9x -21 . . . . . . . . . eliminate parentheses

  27 = 3x . . . . . . . . . . . . . . add 21 -6x

  x = 9 . . . . . . . . . . . . . . . divide by 3

__

b.

The segment lengths are found by substituting the value of 3x in each of the given expressions:

  GH = 3x +3 = 27 +3 = 30

  GK = 3x -7 = 27 -7 = 20

If cosθ=2/3 find cscθ using identities. This is in quad. 1.

Answers

Step-by-step explanation:

cos θ = 2/3

[tex] \quad \twoheadrightarrow\sf {cos \; \theta = \dfrac{Base}{Hypotenuse} } \\ [/tex]

Hence, base = 2 units and hypotenuse = 3 units.

[tex] \quad \twoheadrightarrow\sf { H^2 = B^2 + P^2} \\ [/tex]

[tex] \quad \twoheadrightarrow\sf { P^2 = H^2 - B^2} \\ [/tex]

[tex] \quad \twoheadrightarrow\sf { P^2 = (3)^2 - (2)^2} \\ [/tex]

[tex] \quad \twoheadrightarrow\sf { P^2 = 9- 4} \\ [/tex]

[tex] \quad \twoheadrightarrow\bf { P = \sqrt{5}} \\ [/tex]

Now, we know that :

[tex] \quad \twoheadrightarrow\sf {cosec \; \theta = \dfrac{Hypotenuse}{Perpendicular} } \\ [/tex]

[tex] \quad \twoheadrightarrow\bf{cosec \; \theta = \dfrac{3}{\sqrt{5}} } \\ [/tex]

Therefore, the required answer is 3/5.

three less than the product of two and a number y

can someone plssss translate that into a algebraic expression
plsss ill give you brainiac

Answers

Answer:

[tex]2y-3[/tex]

Step-by-step explanation:

It is saying to subtract 3 from the product of 2 and the variable, y.

Need help please!

1.) m varies directly as a and b; m=10 when a=4 and b=7. Find m when a=11 and b=8.

2.) q varies jointly as x and y. Find q when x=2 and y=5, given that q=90 when x=3 and y=5.

3.) F varies jointly as x and y. If F=1 when x=1/2 and y=1/3, find F when x=2 and y=3.

4.) Let x be proportional to p and q^2, and inversely proportional to r^3. If x=9 when p=4, q=9, and r=3, find x if p=6, q=2, and r=5.

Answers

Answer:

4) v=kx^2/y^3

2= k(4^2)/(3^3)

2 =k16/27

k = 2(27/16) = 27/8

v = (27/8)(3^2)/(2^3 = (27/8)(9/8) = 243/64

v = 243/64 when x=3 and y=2

Step-by-step explanation:

here

F varies jointly as x and y and the value of x is 3 and y is 2.

We have given that,

1.) m varies directly as a and b  m=10 when a=4 and b=7. Find m when a=11 and b=8.

What is the formula?

v=kx^2/y^3

2= k(4^2)/(3^3)

2 =k(16/27)

k = 2(27/16)

k = 27/8

v = (27/8)(3^2)/(2^3)

= (27/8)(9/8)

= 243/64

v = 243/64 when x=3 and y=2.

Therefore we get the value of x is 3 and y is 2.

To learn more about the inverse value visit:

https://brainly.com/question/3831584

#SPJ2

On the same coordinate plane mark all points (x y) that satisfy the rule y=3x-2 SHOW GRAPH

Answers

Answer:

*View the attached graph*

Step-by-step explanation:

Hope it helps!

Please help! It's very confusing to me

Answers

Answer:

b. is the equation and 18 is the answer.

Step-by-step explanation:

the 9 plus b has to equal the 27

18 is the value of b.

How many 12 hours periods (half days) will pass after 25 hours? Enter only the whole number of period that have passed?

Answers

Answer:

2

Step-by-step explanation:

12 + 12 = 24

E D 1389 xo С 76.2° B А Find the value of x. O 38.1 O 30.9 69 O 61.8​

Answers

Based on the intersecting secants theorem, the value of x is: B. 30.9°

What is the Intersecting Secants Theorem?

The intersecting secants theorem states that when two secants intersect, the measure of the angle they form is half the difference of the intercepted arcs.

Thus, based on the intersecting secants theorem, we would have the following:

x = 1/2(138 - 76.2)

x = 1/2(61.8)

x = 30.9°

Learn more about intersecting secants theorem on:

https://brainly.com/question/1626547

Explain how you could find the distance between points (3,6) and (7,6) on the coordinate plane

Answers

Answer:

Count the point on the coordinate plane to the point you want to find the distended from Still stuck? Get 1-on-1 help from an expert tutor now.

Step-by-step explanation:

Calculate the IQR given the box plot​

Answers

Answer:

10

Step-by-step explanation:

The Interquartile Range (IQR) is the difference between Q3 and Q1.

From the diagram we see that Q1 = 40, and Q3 = 50

IQR = Q3-Q1 = 50 - 40 = 10

Prove it Step by Step. Parallelogram Based Question. I will make Brainelist + 50 points ​

Answers

Answer:

(i) ABCD = ABEC

(ii) As BF || AC then BE || AC, so CE = AB.

As AB = DC, then DC = CE

(iii) ΔDGE ≠ ΔCFE so I assume there is a typing error in the question, as

ΔDGC = ΔCFE

As DC = CE (as proved in (i)), AC || BE and DG ⊥ AC and CF ⊥ BE then ΔDGC = ΔCFE

(iv)  As DG ⊥ AC and CF ⊥ BE,  and AC || BE, then DG || CF

(v)  As  AC || BE  then GF || DC.  As DG || CF (as proved in (iv)), then DGFC is a parallelogram.

perform the following division: 3 3/4 ÷ 2/8

Answers

Answer:

15

Step-by-step explanation:

[tex]3\frac{3}{4} / \frac{2}{8} = \frac{15}{4} / \frac{2}{8} = \frac{15}{4} * \frac{8}{2} = \frac{120}{8} = 15[/tex]

what is the volume inside a cylinder 10ft radius 6 ft height

Answers

Answer:

1884.956ft³

Step-by-step explanation:

[tex]volume = \pi {r}^{2} h \\ = \pi \times {10ft}^{2} \times 6ft \\ = 600\pi {ft}^{3} \\ = 1884.956 {ft}^{3} [/tex]

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