Answer:
f(x) = 3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x + [tex]\frac{68}{3}[/tex]
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 - [tex]\frac{2X^{3} }{3}[/tex] - 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 - [tex]\frac{2(1)^{3} }{3}[/tex] - 17(1) + C
8 = 3 - [tex]\frac{2}{3}[/tex] - 17 + C
C =8 - 3 + 17 + [tex]\frac{2}{3}[/tex]
C = 22 + [tex]\frac{2}{3}[/tex]
C =[tex]\frac{66 + 2}{3}[/tex]
C = [tex]\frac{68}{3}[/tex]
f(x) = 3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x + [tex]\frac{68}{3}[/tex]
