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Let f(x)=xsinpix ,\ x >0 . Then for ...

Let `f(x)=xsinpix ,\ x >0` . Then for all natural numbers `n ,\ f^(prime)(x)` vanishes at (a) A unique point in the interval `(n ,\ n+1/2)` (b) a unique point in the interval `(n+1/2,\ n+1)` (c) a unique point in the interval `(n ,\ n+1)` (d) two points in the interval `(n ,\ n+1)`

A

`1+x^(5)`

B

`5x^(4)`

C

`(1)/(1+{g(x)}^(5))`

D

`1+{g(x)}^(5)`

Text Solution

Verified by Experts

Since g is inverse of f,f(g(x))=x
`rArr" "f'(g(x))g'(x)=1`
`rArr" "g'(x)=1+(g(x))^(5)" "(becausef'(x)=(1)/(1+x^(5)))`
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