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Question

For the curve y = 3sin θcosθ,x=eθsinθ,0θπ; tangent is parallel to x-axis, then θ =

A
\N
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B
π2
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C
π4
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D
π6
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Solution

The correct option is C π4
Given y = 3 sin θcosθ, x = eθsinθ
For tangent parallel to x-axis, we should have dydx = 0
dydx = 0 and dxdθ0 and ddθ(3sin2θ2) = 0
3cos2θ=02θ=π2
θ=π4
Note that for θ=π4,dxdθ=eθ[sinθ+cosθ]0.

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