2023 AP Calculus AB FRQ #5

The functions f and g are twice differentiable. The table shown gives values of the functions and their first derivatives at selected values of x.
(a) Let h be the function defined by h(x) = f(g(x)). Find h’(7). Show the work that leads to your answer.
(b) Let k be a differentiable function such that k’(x) = (f(x))^2 · g(x). Is the graph of k concave up or concave down at the point where x = 4 ? Give a reason for your answer.
(c) Let m be the function defined by m(x) = 5*x^3 + ∫ f’(t) dt from 0 to x. Find m(2). Show the work that leads to your answer.
(d) Is the function m defined in part (c) increasing, decreasing, or neither at x = 2 ? Justify your answer.
Intro: 00:00
Problem a: 00:14
Problem b: 02:36
Problem c: 06:57
Problem d: 08:24