Find the local maxima and local minima, if any, of the following functions (ii) g(x) = x^3 − 3x

Question

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be:

(ii). g(x) = x³ − 3x

Answer 1

(ii) g(x) = x³ − 3x

By second derivative test, x = 1 is a point of local minima and local minimum value of g at x = 1 is g(1) = 1³ − 3 = 1 − 3 = −2.

However, x = −1 is a point of local maxima and local maximum value of g at x = −1 is g(1) = (−1)³ − 3 (− 1) = − 1 + 3 = 2.