Find the local maxima and local minima, of the function f(x) = sin x – cos x, 0

Question

Find the local maxima and local minima, of the function f(x) = sin x – cos x, 0 < x <2π. Also find the local maximum and local minimum values.

Philoid · Accepted Answer

We have, f(x) = sin x – cos x, 0 < x <2π

f’(x)= 0 ⇒ cosx+sinx=0

⇒ cosx= -sinx

⇒ tan x= -1

Now, f’’(x) = cosx – sinx

At

is the point of local maximum.

At

is the point of local minimum.

Local maximum value =

Local minimum value =

Find the local maxima and local minima, of the function f(x) = sin x – cos x, 0 < x <2π. Also find the local maximum and local minimum values.