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Question
If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is ______.
Options
`x^4 + 1/x^3 - 129/8`
`x^3 + 1/x^4 + 129/8`
`x^4 + 1/x^3 + 129/8`
`x^3 + 1/x^4 - 129/8`
Solution
If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is `underline(x^4 + 1/x^3 - 129/8)`.
Explanation:
`d/dx f(x) = 4x^3 - 3/x^4`
= f (x) `= int (4x^3 - 3/x^4) dx`
`= 4/4 x^4 - 3/(-3).1/x^3 + C`
`= x^4 + 1/x^3` + C
But, f(2) = 0
`(2)^4 + 1/(2)^3 + C = 0`
`= 16 + 1/8 + C = 0`
⇒ C `= - 129/8`
⇒ f(x) = `x^4 + 1/x^3 - 129/8`
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