Q3 of 168 Page 231

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

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



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