Q. 3 D 3.9( 10 Votes )

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

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


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

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RS Aggarwal - Mathematics