Identify the global extrema of a function

Question

(Calculator allowed)

Identify the global extrema of the function

f(x) = -5x⁴ + 3x³ + 2x² + x on the interval -1≤ x ≤ 1.

A) This function has no global extrema

B) Global maximum: x = 1, global minimum: x = -1

C) Global maximum: x = 0.786, global minimum: x = 1

D) Global maximum: x = 0.786, global minimum: x = -1

Answer 1

The usual way to do this is to find the critical points: the ones where the derivative f'(x) = 0.

f'(x) = -20x^3+9x^2+4x+1, so if you want to you can check whether there are any zeros between 1 and -1 with your calculator. You can find the largest and smallest values of f at these, and compare to f(1) and f(-1) to find the global extrema.

Since this is multiple choice though, it might be faster to "cheat" and plug in the values given in B,C, D to see which is the global max and which is the global min.