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 <2\pi$

Question

$\begin{array}{1 1} Maxima =\sqrt 3\; Minima = -\sqrt 2 \\ Maxima =\sqrt 2\; Minima = -\sqrt 2 \\ Maxima =\sqrt 2 Minima = \sqrt 2 \\ Maxima =\sqrt 2 Minima = -\sqrt 3 \end{array} $