Integrate twice.
Remember the anti-derivative rule for polynomials:
[tex]\int x^n dx = \frac{x^{n+1}}{n+1} + C[/tex]
[tex]f'(x) = \int (-2 +24x -12x^2) dx = -2x + 12x^2 -4x^3 + C \\ \\ f'(0) = 16, C = 16 \\ \\ f(x) = \int (16 -2x+12x^2-4x^3) dx = 16x -x^2 + 4x^3 - x^4 + C \\ \\ f(0) = 7, C = 7[/tex]
Answer:
[tex]f(x) = 7 + 16x -x^2 + 4x^3 - x^4 [/tex]
