ap-calculus-ab 1998 Q3

ap-calculus-ab · USA · free-response_formB Stationary points and optimisation Solve trigonometric equation for solutions in an interval

Let $f$ be the function defined for $\frac { \pi } { 6 } \leqq x \leq \frac { 5 \pi } { 6 }$ by $f ( x ) = x + \sin ^ { 2 } x$. (a) Find all values of $x$ for which $f ^ { \prime } ( x ) = 1$. (b) Find the $x$-coordinates of all minimum points of $f$. Justify your answer. (c) Find the $x$-coordinates of all inflection points of $f$. Justify your answer.

$\begin{cases} 1 : & \text { sets } y ^ { \prime } = b e ^ { b x } ( 1 + b x ) = 0 \\ 1 : & \text { solves student's } y ^ { \prime } = 0 \\ 1 : & \text { evaluates } y \text { at a critical number } \\ & \text { and gets a value independent of } b \end{cases}$

Let $f$ be the function defined for $\frac { \pi } { 6 } \leqq x \leq \frac { 5 \pi } { 6 }$ by $f ( x ) = x + \sin ^ { 2 } x$.
(a) Find all values of $x$ for which $f ^ { \prime } ( x ) = 1$.
(b) Find the $x$-coordinates of all minimum points of $f$. Justify your answer.
(c) Find the $x$-coordinates of all inflection points of $f$. Justify your answer.

Paper Questions

Q1 Q2 Q3 Q4 Q5