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What is the value of p for which the fun...

What is the value of p for which the funtion
`f(X)=p sinx+(sin 3x)/(3)`
has an extremum at `x=(pi)/(3)`?

A

0

B

1

C

`-1`

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
Let f(x)`= sinx +(sin 3x)/(3)` ltrbgt Diferentiate both side w.r.t (x)
`rarr f(x) = p cos x+(3 cos 3x)/(3)=p cos x + cos 3x`
it is given that f(X) has extremum value at x= `pi//3`
`therefore f((pi)/(3))=0`
`rarr p cos (pi)/(3)+ cos pi =0`
`rarr (p)/(2)-1 =0 rarr p=2`
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