Question

Find the points at which the function f given byhas

(i) local maxima (ii) local minima

(ii) point of inflexion

Answer 1

The given function is

Now, for values of x close toand to the left of Also, for values of x close to and to the right of

Thus, is the point of local maxima.

Now, for values of x close to 2 and to the left of Also, for values of x close to 2 and to the right of 2,

Thus, x = 2 is the point of local minima.

Now, as the value of x varies through −1,does not changes its sign.

Thus, x = −1 is the point of inflexion.