Question

determine whether the statement is true or false. if f has an absolute maximum value at c, then f '(c) = 0.

Answer 1

If f has an absolute maximum value at c, then f '(c) = 0 is true.

Step-by-step explanation:

True. If the function f has an absolute maximum value at c, then the derivative of f at c, denoted as f'(c), must be equal to zero.

This is because at an absolute maximum point, the function stops increasing and starts decreasing, which means the slope of the function is zero at that point. Therefore, f'(c) must be equal to zero.