ap-calculus-ab 2008 Q4

ap-calculus-ab · USA · free-response_formB Chain Rule Chain Rule Combined with Fundamental Theorem of Calculus

The functions $f$ and $g$ are given by $f ( x ) = \int _ { 0 } ^ { 3 x } \sqrt { 4 + t ^ { 2 } } d t$ and $g ( x ) = f ( \sin x )$. (a) Find $f ^ { \prime } ( x )$ and $g ^ { \prime } ( x )$. (b) Write an equation for the line tangent to the graph of $y = g ( x )$ at $x = \pi$. (c) Write, but do not evaluate, an integral expression that represents the maximum value of $g$ on the interval $0 \leq x \leq \pi$. Justify your answer.

$\left\{ \begin{array} { l } 1 : \frac { d V } { d t } = 2000 \text { and } \frac { d r } { d t } = 2.5 \\ 2 : \text { expression for } \frac { d V } { d t } \\ 1 : \text { answer } \end{array} \right.$

The functions $f$ and $g$ are given by $f ( x ) = \int _ { 0 } ^ { 3 x } \sqrt { 4 + t ^ { 2 } } d t$ and $g ( x ) = f ( \sin x )$.
(a) Find $f ^ { \prime } ( x )$ and $g ^ { \prime } ( x )$.
(b) Write an equation for the line tangent to the graph of $y = g ( x )$ at $x = \pi$.
(c) Write, but do not evaluate, an integral expression that represents the maximum value of $g$ on the interval $0 \leq x \leq \pi$. Justify your answer.

Paper Questions

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