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:

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: f (x) = x 2

Philoid · Accepted Answer

f(x) = x²

⇒ f’(x) = 2x

Now, f’(x) = 0

⇒ x = 0

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

⇒ f’’(0) = 2, which is positive.

Then, by second derivative test,

⇒ x = 0 is point of local maxima and local minima of f at x = 0 is f(0) = 0.

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:f (x) = x2

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:
f (x) = x²