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:

(i). f(x) = x^2​

Answer 1

Thus, x = 0 is the only critical point which could possibly be the point of local maxima or local minima of f.

We have,  which is positive.

Therefore, by second derivative test, x = 0 is a point of local minima and local minimum value of f at x = 0 is f(0) = 0.