Question

What is the total number of relative maximum and minimum points of the function whose derivative for all x is given by f ‘ (x) = x(x – 3)^2 (x + 1)^4 ?

Answer 1

The total number of relative maximum and minimum points of the function depends on the number of roots in its derivative.

Step-by-step explanation:

The function's derivative f'(x) = x(x – 3)^2 (x + 1)^4 helps us determine the relative extrema of the function.

To find the total number of relative maximum and minimum points, we need to analyze the behavior of the derivative. The derivative is equal to zero when x = 0, x = 3, and x = -1.

Since the function has three roots, it means there can be up to three possible relative extrema.