Advanced Placement (AP) College

The slope field for a certain differential equation is shown above. Which of the following statements about a solution y = f(x) to the differential equation must be FALSE?

A) The graph of the particular solution that satisfies f(1)=−1 is concave down on the interval 0
B) The graph of the particular solution that satisfies f(−1)=1 is concave up on the interval −1
C) The graph of the particular solution that satisfies f(0)=0 is concave up on the interval −1
D) The graph of the particular solution that satisfies f(0)=0 has a point of inflection at x=0

The Slope Field For A Certain Differential Equation Is Shown Above. Which Of The Following Statements

Answers

Answer 1

The statement about a solution y = f(x) to the differential equation that must be FALSE is C) The graph of the particular solution that satisfies f(0)=0 is concave up on the interval −1.

How to explain the graph

Based on the information, the graph of the specific solution to the equation f(1)=1 is concave downward on the range 0–1.

Concave up on the interval 1, the graph of the particular solution that fulfills f(1)=1.

Therefore, the graph of the particular solution that satisfies f(0)=0 is concave up on the interval −1 is false.

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