ap-calculus-ab 1999 Q2

ap-calculus-ab · USA · free-response_formB Factor & Remainder Theorem Custom Operation or Property Verification
Given the two functions $f$ and $h$ such that $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12$ and $h ( x ) = \left\{ \begin{array} { l } \frac { f ( x ) } { x - 3 } , \text { for } x \neq 3 \\ p , \text { for } x = 3 . \end{array} \right.$ (a) Find all zeros of the function $f$. (b) Find the value of $p$ so that the function $h$ is continuous at $x = 3$. Justify your answer. (c) Using the value of $p$ found in (b), determine whether $h$ is an even function. Justify your answer.
The shaded region, $R$, is bounded by the graph of $y = x ^ { 2 }$ and the line $y = 4$, as shown in the figure above. 
Given the two functions $f$ and $h$ such that $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12$ and $h ( x ) = \left\{ \begin{array} { l } \frac { f ( x ) } { x - 3 } , \text { for } x \neq 3 \\ p , \text { for } x = 3 . \end{array} \right.$
(a) Find all zeros of the function $f$.
(b) Find the value of $p$ so that the function $h$ is continuous at $x = 3$. Justify your answer.
(c) Using the value of $p$ found in (b), determine whether $h$ is an even function. Justify your answer.
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6 Q7