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

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