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) = sin x – cos x, 0 < x < 2π

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) = sin x – cos x, 0 < x < 2π

Philoid · Accepted Answer

f (x) = sin x – cos x, 0 < x < 2π

f’(x) = cosx + sinx

Now, f’(x) = 0

⇒ cosx + sinx = 0

⇒ cosx = -sinx

⇒ tanx = -1

’(x) = -sinx + cosx

Then, by second derivative test,

is point of local maxima and the local maximum value of f at is

And,

is point of local minima and the local minimum value of f at is

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) = sin x – cos x, 0 < x < 2π

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) = sin x – cos x, 0 < x < 2π