Answer:
f(x) = -x⁴ + 4x³ - x² + 18x + 4
Step-by-step explanation:
If we take the integral of f''(x) with respect to x, we get that f'(x)= -2x + 12x² - 4x³ + C.
- Substituting in f'(0)=18, we get C=18.
- So, f'(x) = -2x + 12x² - 4x³ + 18.
If we take the integral of f'(x) with respect to x, we get that f(x) = -x² + 4x³ - x⁴ + 18x + C.
- Substituting in f(0) = 4, we get C=4.
- So, f(x) = -x⁴ + 4x³ - x² + 18x + 4
