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Slope of tangent to the curve y=2e^(x)si...

Slope of tangent to the curve `y=2e^(x)sin((pi)/(4)-(x)/(2))cos((pi)/(4)-(x)/(2))`, where `0le xle2pi` is minimum at x =

A

0

B

`pi`

C

`2pi`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
The slope of the tangent to the curve
`y=2e^(x)sin((pi)/(4)-(x)/(2))cos((pi)/(4)-(x)/(2))=e^(x)cosx`
`S=(dy)/(dx)=e^(x)(-sinx+cosx)`
Now, `(dS)/(dx)=e^(x)(-sinx+cosx-cosx-sinx)`
`=-2e^(x)sinx`
`(dS)/(dx)=0 rArr -2e^(x)sin x=0`
`rArr" "x=0,pi,2pi(because 0le xle 2pi)`
Value of S at x = 0 is 1 , value of S at `x=pi` is `-e^(x)`
Value of S at `x=2pi` is `e^(2pi)`
`therefore" S is minimum at "x=pi`.
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