Answer the questions for the function f(x) = 4x^4 - 48x^3
a. Find formulas for f'(x) and f''(x).
f'(x) = 16x^3 - 144x^2
f''(x) = 48x^2 - 288x
Enter f(x), f'(x), and f''(x) into your grapher to examine the table.
b. Set f'(x) = 0 to find the critical numbers. One of the critical numbers of f(x) is x = 0. What is the other critical number?
x = 9
What is true about f(x) at this positive critical number? Select the correct choice below and, if necessary, fill in the answer boxes within your choice.
A. The graph of f is concave up and f has a relative maximum at ( , ).
B. The graph of f is concave up and f has a relative minimum at ( , ).
C. The graph of f is concave down and f has a relative maximum at ( , ).
D. The graph of f is concave down and f has a relative minimum at ( , ).
E. No conclusion can be made.