Find the points of local maxima or local minima, if any, of the following functions, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be:

Question

Philoid · Accepted Answer

We have, f(x) = 2 sin x – x

Differentiate w.r.t x, we get,

f ‘(x) = 2cos x – 1 = 0

For, the point of local maxima and minima,

f ’(x) = 0

cos x =

= x =

At x = f ’(x) changes from –ve to + ve

Since, x = is a point of Minima with value =

At x = f ‘ (x) changes from –ve to + ve

Since, x = is point of local maxima with value =

Hence, local max value f

local min value f