ap-calculus-ab 2001 Q5

ap-calculus-ab · Usa · free-response Stationary points and optimisation Determine parameters from given extremum conditions
A cubic polynomial function $f$ is defined by $$f(x) = 4x^{3} + ax^{2} + bx + k$$ where $a$, $b$, and $k$ are constants. The function $f$ has a local minimum at $x = -1$, and the graph of $f$ has a point of inflection at $x = -2$.
(a) Find the values of $a$ and $b$.
(b) If $\displaystyle\int_{0}^{1} f(x)\,dx = 32$, what is the value of $k$? 
A cubic polynomial function $f$ is defined by
$$f(x) = 4x^{3} + ax^{2} + bx + k$$
where $a$, $b$, and $k$ are constants. The function $f$ has a local minimum at $x = -1$, and the graph of $f$ has a point of inflection at $x = -2$.\\
(a) Find the values of $a$ and $b$.\\
(b) If $\displaystyle\int_{0}^{1} f(x)\,dx = 32$, what is the value of $k$?
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6