ap-calculus-bc 2012 Q12

ap-calculus-bc · Usa · practice-exam Differential equations Qualitative Analysis of DE Solutions
The points $( - 1 , - 1 )$ and $( 1 , - 5 )$ are on the graph of a function $y = f ( x )$ that satisfies the differential equation $\frac { d y } { d x } = x ^ { 2 } + y$. Which of the following must be true?
(A) $( 1 , - 5 )$ is a local maximum of $f$.
(B) $( 1 , - 5 )$ is a point of inflection of the graph of $f$.
(C) $( - 1 , - 1 )$ is a local maximum of $f$.
(D) $( - 1 , - 1 )$ is a local minimum of $f$.
(E) $( - 1 , - 1 )$ is a point of inflection of the graph of $f$.
The points $( - 1 , - 1 )$ and $( 1 , - 5 )$ are on the graph of a function $y = f ( x )$ that satisfies the differential equation $\frac { d y } { d x } = x ^ { 2 } + y$. Which of the following must be true?

(A) $( 1 , - 5 )$ is a local maximum of $f$.

(B) $( 1 , - 5 )$ is a point of inflection of the graph of $f$.

(C) $( - 1 , - 1 )$ is a local maximum of $f$.

(D) $( - 1 , - 1 )$ is a local minimum of $f$.

(E) $( - 1 , - 1 )$ is a point of inflection of the graph of $f$.