Question

If f'(x) = 12x^3 - 2x^2 - 17 and f(1) = 8 , find f(x).

Answer 1

f(x) = 3x⁴ -
`(2X^(3) )/(3)` - 17x +
`(68)/(3)`

Explanation:

To find f'(x), we will follow the steps below:

We will start by integrating both-side of the equation

∫f'(x) = ∫(12x^3 - 2x^2 - 17)dx

f(x) = 3x⁴ -
`(2X^(3) )/(3)` - 17x + C

Then we go ahead and find C

f(1) = 8

so we will replace x by 1 in the above equation and solve for c

f(1) = 3(1)⁴ -
`(2(1)^(3) )/(3)` - 17(1) + C

8 = 3 -
`(2)/(3)` - 17 + C

C =8 - 3 + 17 +
`(2)/(3)`

C = 22 +
`(2)/(3)`

C =
`(66 + 2)/(3)`

C =
`(68)/(3)`

f(x) = 3x⁴ -
`(2X^(3) )/(3)` - 17x +
`(68)/(3)`