Question

Find the relative extrema of the function, if they exist. f(x)=−4x 3+4

A) Relative minimum at (0,4)
B) Relative maximum at (0,4)
C) Relative maximum at (0,−4)
D) No relative extrema exist

Answer 1

The function has a relative maximum at (0,4).

Step-by-step explanation:

The function is given by f(x) = -4x^3 + 4. To find the relative extrema, we need to find the critical points of the function by finding where the first derivative is equal to zero or undefined. Taking the derivative of f(x), we get f'(x) = -12x^2. Setting this equal to zero, we find x = 0. Since the second derivative is negative at x = 0, the position is a relative maximum. Therefore, the answer is option B) Relative maximum at (0,4).