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:

Question

Philoid · Accepted Answer

h(x) = sin x + cos x,

h’(x) = cosx - sinx

Now, h’(x) = 0

⇒ cosx - sinx = 0

⇒ cosx = sinx

⇒ tanx = 1

h’’(x) = -sinx – cosx = -(sinx + cosx)

Then, by second derivative test,

is point of local maxima and local minima of h at is