The value of the derivative at the maximum or minimum for a continuous function must be zero.
What happens with the derivative at the maximum of minimum?So, remember that the derivative at a given value gives the slope of a tangent line to the curve at that point.
Now, also remember that maximums or minimums are points where the behavior of the curve changes (it stops going up and starts going down or things like that).
If you draw the tangent line to these points, you will see that you end with horizontal lines. And the slope of a horizontal line is zero.
So we conclude that the value of the derivative at the maximum or minimum for a continuous function must be zero.
If you want to learn more about maximums and minimums, you can read:
https://brainly.com/question/24701109
I well give u brainliest
What are the x- and y-intercepts for the linear equation 2x – 4y = 8 ?
Question 6 options:
(4,0) and (0,-2)
(2,0) and (0,4)
(-2,0) and (4,0)
(-2,0) and (0,4)
The answer is a. (4,0) and (0,-2)
A city that has an elevation of 15 meters is closer to sea level than a city that has an elevation of -10 meters.
Answer:
Step-by-step explanation: Your answer will be -10 because even though -10 is much lower than 15 it’s still closer to sea level.
Determine the type of symmetry of r =5-sin11ø from the equation, if any. Make sure to confirm graphically. Symmetric with respect to the:
A) pole
B) line /2
C) polar axis
D) none of these
well, let me not bore you to death on how we test it and test it.
[tex]\underline{\textit{testing for symmetry to the }\frac{\pi }{2}~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=5-sin(11\theta )\implies (-r)=5-sin[11(-\theta )]\implies -r=5-sin(-11\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=5-\stackrel{\downarrow }{[-sin(11\theta )]}}\implies\implies r=-5-sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=5-sin(11\theta )\implies r=5-sin[11(-\theta )]\implies r=5-sin(-11\theta ) \\\\\\ r=5-[-sin(11\theta )]\implies r=5+sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underline{\textit{testing for symmetry to the pole}\qquad \qquad r=-r} \\\\\\ r=5-sin(11\theta )\implies -r=5-sin(11\theta )\implies r=-5+sin(11\theta )\qquad \textit{no dice}[/tex]
so the symmetry tests didn't pass, notice the picture below though, looks a bit deceiving, it looks as if it'd have π/2 symmery, but it doesn't show in the test.
JKL and RST are shown below. Which of the following statements is true? Look at picture.
Answer:
Triangle JLK congruent to Triangle RTS is the only true statement
Step-by-step explanation:
AngleJKL is not corresponding to AngleRTS because AngleRTS is a right angle and AngleJKL is not.
The triangles are congruent by HL because one leg and the hypotenuse are congruent.
Triangle congruence can be determined so the third statement is incorrect.
TR is not congruent to KJ. TR=3.7 and KJ=4.5
A team sells their jerseys for 40% more than it costs to have them made. What is the selling price of a jersey that cost the team $25.
Answer:
$35.
Step-by-step explanation:
SP = 25 + 0.40*25
= 25 + 10
= $35.
HELPPPPP PLEASE I DONT UNDERSTANDDDD
Answer:
Step-by-step explanation:
Solve for the equation equal to y
[tex]3x+4y=12\\4y=-3x+12\\y=\frac{-3}{4}+\frac{12}{4}[/tex]
The slope here is -3/4. The slope of a line perpendicular to the original has a negated and inverted slope. Therefore the slope is 4/3
Make an accurate drawing of two rectangles with the same perimeter, but different areas. Indicate the dimensions of the rectangles, as well as the perimeter and the area in each figure.
What is the solution to use the following equation 5(2x-6)+20=10
Answer:
first you distribute the five making it 10x-30+20=10
second you combine like terms making it 10x-10=10
third you isolate the variable making it 10x=20
Finally you divide both terms by ten giving you x=2 as your answer.
Find the volume. Please help! Thanks!
hehe
Volume of a Square Pyramid: 1/3 x length x width x height
Length = 2
Width = 2
Height = 3
Volume = 1/3 x 2 x 2 x 3
Volume = 1/3 x 4 x 3
Volume = 1/3 x 12
Volume = 4
Volume = 4 cm^3
Hope this helps!
could someone explain to me how to multiple/divide equations in scientific notation im super confused :(
A gas tank holds exactly 14 gallons of gas. If the tank is 2/3 empty, how many gallons remain in the tank?
2/3 empty would mean 1/3 of the total would remain:
14 gallons x 1/3 = 4 2/3 gallons are left in the tank
10 cm equal to cm can you help me.
Answer:
1000cm
Step-by-step explanation:
there are 100cm in a meter. so we multiply 10 by 100 to get the amount of centimeters in 10 meters which is 1000cm
Answer: There Are 1000 Centimeters(Cm) In 10 Meters(M)
the ratio of the length of shantels pool to the length of juan's pool is 3 to 5 shantels pool is 30 meters how long is Juan’s pool
Step-by-step explanation:
the ratio of the pool lengths is 3/5.
that means for every 3 meters of length on Shantel's pool, there are 5 meters of length on Juan's pool.
it the other way around : to get to the size of Shantel's pool, every 5 meters of length on Juan's pool are converted to 3 meters.
x = length of Juan's pool
x × 3/5 = 30
3x = 150
x = 50 meters
you see the relationship ?
3/5 = 30/50 = 300/500 = ...
but it is true for any factor
3/5 = 15/25 = 24/40 = 6/10 = ...
once you see the factor for one part of the ratio, you know there is the same factor for the other part (or parts) of the ratio. otherwise the ratio would not stay the same and keep the relationship.
Find the LCM of 20, 35 & 50.
Answer:
Answer: LCM of 20,35 and 50 is 1400
Step-by-step explanation:
solve ~
[tex]x {}^{2} - 5x + 6 = 0[/tex]
don't spam .-.
thankyou ~
Δ = (-5)² - 4*1*6 = 25 - 24 = 1 = 1²
x' = (5 + 1) / (2*1) = 6/2 = 3
x" = (5-1) / (2*1) = 4/2 = 2
2 solutions : 2 and 3
x² - 5x + 6 = (x - 2) (x - 3)
A manager drew this box-and-whisker plot to represent the number of minutes each of the company's 360 employees took on their break.
How many employees took a break that lasted between 37 and 41 minutes?
Select from the drop-down menu to correctly complete the statement.
About (blank) employees took a break that lasted between 37 and 41 minutes.
36
90
120
180
Answer:
on k12 im pretty sure its 90
Step-by-step explanation:
there is 360 minutes and between the 37 and 41 (this took me a while ) then you should get 90!!!!! hope this helped
help please .and thank u :)
Answer:
5/8
Step-by-step explanation:
because 1 minus 3/8 is 5/8
Find the area. 9 cm 3 cm 12 cm 15_cm 3 cm
Answer:
What shape is the object in question?
Ms. Gardner is thinking of a number
The number is even.
It is not divisible by 6
It is not divisible by 7
it is not greater than 81
It is not less than 64
Answer:
74
Step-by-step explanation: 74 is not divisible by 6 or 9not nor 7 and it's less than 81 and greater than 64
Susan reads a book at a rate of 1 page every 3 minutes. If her reading rate remal
the same, which method could be used to determine the number of minutes for t
to read 18 pages?
10+500000000 wats the answer
Answer:
500,000,010
Step-by-step explanation:
The 10 would be added to the last 2 digits (00) of the number. Therefore, the last 2 digits (00) plus 10 would be 10. The remainder of the number would remain the same, making the answer: 500,000,010
210 cartons is __% of 60 cartons
Answer:
should definitely be 28.56
Please answer this relatively quickly, I'm not in very much of a rush but would like to get this done.
Answer: 6
Step-by-step explanation:
Because you have to multiply then remove the fraction and set equal to 0 and solve for x which I’m pretty sure gives u 6
write an expression to m+m+m+m that is a product of a coefficient and a variable
[tex]m+m+m+m=(1+1+1+1)m=4m[/tex]
Find the area of the 2.5 m circle using 3.14 or 2/7 four pi
Answer:
Formula for area of circle;
A = π[tex]r^{2}[/tex]
Where 'π' represents pi (22/7 or 3.14), and 'r' is the radius which is being squared.
Plug in your values:-
A = π[tex]r^{2}[/tex]
A = 3.14(2.5^2)
A = 3.14(6.25)
A = 19.625 meters is your answer.
Find the missing side length using the Pythagorean Theorem.
a²+6² = ²
The missing length is 18
Using Pythagorean rule
Hyp^2 = Opp^2 + adj^2
Opp^2 = hyp^2 - adj^2
Opp^2 = 30^2 - 24^2
Opp^2 = 900 - 576
Opp^2 = 324
Opp = sqrt ( 324 )
Opp = 18
An assembly line consists of 21 tasks grouped into 5 workstations. The sum of the 21 task times is 90 minutes. The largest assigned cycle time is 20 minutes. What is the efficiency of this line?
Answer:
ok
Step-by-step explanation:
1: The number of hours, h, spent studying and the score s, on a test (find the independent variable and the dependent variable.
Answer:
independent - number of hours (h)
dependent - the score (s)
Step-by-step explanation:
how many cubic inches of hot air would be needed to completely inflate a 12 in diameter beach ball
Answer:
904.78 cubic inches
Step-by-step explanation:
Since a beach ball is a sphere, use the formula for volume, V = 4/3 * pi * r^3 to find the volume of the beach ball, using 6 for radius since diameter is two times the radius and the diameter is 12 inches. 4/3 * pi * 6^3 = 904.78, so that many cubic inches of air would be needed to inflate the beach ball.
Hopefully this helps- let me know if you have any questions!
The height h(t) (in feet) of the seat of a child’s swing above ground level is given by the equation
below where t is the time in seconds after the swing is set in motion.
ℎ() = −1.1 cos ((2/3) ) + 3.1
a. Find the maximum and minimum height of the swing.
b. When is the first time after t = 0 that the swing is at a height of 3 feet?
c. When is the second time after t = 0 that the swing is at a height of 3 ft?
Answer: See below
Step-by-step explanation:
The function of the seat’s height from the ground level is given as,
[tex]h(t)=-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1[/tex]
Here, t denotes the time.
(a) The height will be maximum or minimum when the derivative of the function of height is equal to zero.
[tex]\begin{aligned}h^{\prime}(t) &=0 \\\frac{d}{d t}\left(-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1\right) &=0 \\-1.1 \times \frac{2 \pi}{3}\left(-\sin \left(\frac{2 \pi}{3} t\right)\right) &=0 \\t &=0,1.5\end{aligned}[/tex]
The height of the seat at time t = 0 s can be determined as,
[tex]\begin{aligned}h(0) &=-1.1 \cos \left(\frac{2 \pi}{3}(0)\right)+3.1 \\&=2 \mathrm{ft}\end{aligned}[/tex]
Therefore, the maximum height of the swing is 4.2 ft and the minimum height of the swing is 2 ft.
(b) The height of the swing is given as,
[tex]\begin{aligned}h &=3 \mathrm{ft} \\-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1 &=3 \\t &=0.7 \mathrm{~s}\end{aligned}[/tex]
Therefore, the first time after t = 0 s that the swing’s height of 3 ft is 0.7 s.
(c) The height of the swing is given as,
[tex]\begin{aligned}h &=3 \mathrm{ft} \\-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1 &=3 \\\frac{2 \pi}{3} t &=1.47976+2 \pi \\t &=3.7 \mathrm{~s}\end{aligned}[/tex]
Therefore, the second time after t = 0 s that the swing’s height of 3 ft is 3.7 s.