Q. 85.0( 2 Votes )

# Find the points of local maxima or local minima, if any, of the following functions, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be:

f(x) = sin x – cos x, 0 < x < 2π

Answer :

We have, f(x) = sin x – cos x

Differentiate w.r.t x, we get,

f ‘(x) = cos x + sin x

For, the point of local maxima and minima,

f ’(x) = 0

= cos x = – sin x => tan x = – 1 = x =

Again differentiate w.r.t x

f ’’(x) = – sin x + cos x

f ”= – sin + cos = –

f ”= – sin + cos = –

Therefore, by second derivative test, x = is a point of local maxima and the local maximum of f at x = is

F” = sin – cos =

F” = sin – cos =

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PREVIOUSFind the points of local maxima or local minima, if any, of the following functions, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be:f(x) = sin 2x, 0 < x < πNEXTFind the points of local maxima or local minima, if any, of the following functions, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be:f(x) = cos x, 0 < x < π

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