The point in the interval [0,2π] where f(x)=exsinx 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+cosx+sinxexAndf′(x)=−sinxex+cosxex+cosxex+sinxcosxex.Now,f′(x)=2cosxcosxex=0⇒cosx=0⇒x=π2.Also,f′(x)=−2sinxex+2cosxex=−ve ∴ Slope is maximum at x=π2. Hence (b) is the correct answer.