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If d/(dx)f(x)=4x^3-3/(x^4)such that f(2...

If `d/(dx)f(x)=4x^3-3/(x^4)`such that `f(2)=0.`Then f(x) is

A

`x^(4)+(1)/(x^(3))-(129)/(8)`

B

`x^(3)+(1)/(x^(4))+(129)/(8)`

C

`x^(4)+(1)/(x^(3))+(129)/(8)`

D

`x^(3)+(1)/(x^(4))-(129)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `(d)/(dx)f(x)=4x^(3)-(3)/(x^(4))`
`rArr" Anti - derivative of "(4x^(3)-(3)/(x^(4)))=f(x)`
`therefore" "f(x)=int(4x^(3)-(3)/(x^(4)))dx=4intx^(3)dx-3 int x^(-4)dx`
`rArr" "f(x)=4((x^(4))/(4))-3 ((x^(-3))/(-3))+C=x^(4)+(1)/(x^(3))+C`
Also, `f(2)=0`
`therefore" "f(2)=(2)^(4)+(1)/((2)^(3))+C`
`rArr" "16+(1)/(8)+C=0 rArr C=-(16+(1)/(8))`
`rArr" "C=-(129)/(8)`
`therefore" "f(x)=x^(4)+(1)/(x^(4))-(129)/(8).`
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