If f(x)=int0^x(sint)/t dt ,x >0, then...

If `f(x)=int_0^x(sint)/t dt ,x >0,` then

A

f(x) has a local maxima at x =`npi(n=2k,kin I^(+))`

B

f(x) has a local minimum at x =`npi(n=2k,kin I^(+))`

C

f(x) has neither maxima nor minima at x =`npi(n in I^(+))`

D

f(x) has local maxima at x =`npi(n=2k-1,k in I^(+))`

Text Solution

Verified by Experts

The correct Answer is:

2,4

`f(x) =(sinx )/(x)`
`for f(x)=0,(sinx)/(x)=0 or x =npi,(n in I ,n ne0)`
`f(x)=(xcosx-sinx)/(x^(2))`
`f(npi)=(cosnpi)/(npi)lt0if n=2k -1and gt0nif n =2k,kin I^(+)`
Hence f(X) has local maxima at `x = npi` , where n=2k -I and local minima at `x =npi, n =2k` where `k in I^(+)`

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