AP Calculus AB / Differential Equations / Question No. 25

25. 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?

The graph of the particular solution that satisfies \( f(2) = -2 \) has a relative minimum at \( x = 2 \).

The graph of the particular solution that satisfies \( f(-1) = -1 \) is concave up on the interval \( -2 < x < 1 \).

The graph of the particular solution that satisfies \( f(1) = -2 \) is linear.

The graph of the particular solution that satisfies \( f(-1) = 2 \) is concave up on the interval \( -3 < x < 3 \).

Answer is: option2

The graph of the particular solution that satisfies \( f(-1) = -1 \) is concave up on the interval \( -2 < x < 1 \).

Solution:

The graph of the particular solution that satisfies \( f(-1) = -1 \) is concave up on the interval \( -2 < x < 1 \).

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