ap-calculus-ab 2006 Q6

ap-calculus-ab · USA · free-response_formB Standard Integrals and Reverse Chain Rule Finding a Function from an Integral Equation

Let $f$ be a differentiable function, defined for all real numbers $x$, with the following properties. (i) $f ^ { \prime } ( x ) = a x ^ { 2 } + b x$ (ii) $f ^ { \prime } ( 1 ) = 6$ and $f ^ { \prime \prime } ( 1 ) = 18$ (iii) $\int _ { 1 } ^ { 2 } f ( x ) d x = 18$
Find $f ( x )$. Show your work.

Let $f$ be a differentiable function, defined for all real numbers $x$, with the following properties.
(i) $f ^ { \prime } ( x ) = a x ^ { 2 } + b x$
(ii) $f ^ { \prime } ( 1 ) = 6$ and $f ^ { \prime \prime } ( 1 ) = 18$
(iii) $\int _ { 1 } ^ { 2 } f ( x ) d x = 18$

Find $f ( x )$. Show your work.

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6