Find the local maxima and local minima, if any, of the following functions. (v) f(x) = x^3 − 6x^2 + 9x + 15

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:

(v) f(x) = x³ − 6x² + 9x + 15

Answer 1

(v) f(x) = x³ − 6x² + 9x + 15

Therefore, by second derivative test, x = 1 is a point of local maxima and the local maximum value of f at x = 1 is f(1) = 1 − 6 + 9 + 15 = 19.

However, x = 3 is a point of local minima and the local minimum value of f at x = 3 is f(3) = 27 − 54 + 27 + 15 = 15.