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Question

The point in the interval [0,2π] where f(x)=ex sin x has maximum slope, is


A

π/4

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B

π/2

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C

π

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D

3 π/2

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Solution

The correct option is B

π/2


We have, f(x)=ex+cos x+sin x exAnd f(x)=sin x ex+cos xex+cos x ex+sin x cos xex.Now,f(x)=2 cos x cos x ex=0cos x=0x=π2.Also,f(x)=2 sin xex+2 cos xex=ve
Slope is maximum at x=π2.

Hence (b) is the correct answer.

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