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) = sin 2x

Differentiate w.r.t x, we get,

f ‘(x) = 2cos 2x, 0 < x,π

For, the point of local maxima and minima,

f ’(x) = 0

= 2x =

= x =

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

Since, x = is a point of Maxima

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

Since, x = is point of Minima.

Hence, local max value f = 1

local min value f = – 1

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:f(x) = sin 2x, 0 < x < π

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:
f(x) = sin 2x, 0 < x < π