Question

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

Answer 1

Answer:

f(x) =  3x⁴ - $\frac{2X^{3} }{3}$ - 17x +  $\frac{68}{3}$

Step-by-step 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 - $\frac{2X^{3} }{3}$ - 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 - $\frac{2(1)^{3} }{3}$ - 17(1) + C

8 = 3 - $\frac{2}{3}$ - 17 + C

C =8 - 3 + 17 + $\frac{2}{3}$

C = 22 +  $\frac{2}{3}$

C =$\frac{66 + 2}{3}$

C = $\frac{68}{3}$

f(x) =  3x⁴ - $\frac{2X^{3} }{3}$ - 17x +  $\frac{68}{3}$