Question

If f'(x) = `2 - 5/x^4` and f(1) = `14/3`, then f(-1) = ______

पर्याय

• 0

• `11/3`

• `(-14)/3`

• `(-8)/3`

Answer 1

If f'(x) = `2 - 5/x^4` and f(1) = `14/3`, then f(-1) = `underline((-8)/3)`.

Explanation:

f'(x) = `2 - 5/x^4` 

∴ f(x) = `int (2 - 5/x^4)dx = 2x + 5/(3x^3) + c`

f(1) = 2(1) + `5/(3(1)^3) + c`

⇒ `14/3 = 2 + 5/3 + c ⇒ c = 1`

∴ f(x) = `2x + 5/(3x^3) + 1`

f(-1) = `2(-1) + 5/(3(-1)^3) + 1`

`= -2 - 5/3 + 1 = (-8)/3`