Question

Find f such that f'(x) = 5x² + 9x - 7 and f(0) = 8.

Answer 1

Answer:

$\frac{5}{3}x^3+\frac{9}{2}x^2-7x+8$

Step-by-step explanation:

Integrate your function with respect to x to get the non-differentiated form.

$\int(5x^2+9x-7)dx=\frac{5}{3}x^3+\frac{9}{2}x^2-7x+c$

Plug in your known value of x to get your value for your constant

$f(0) = 8\\ \frac{5}{3}(0^3)+\frac{9}{2}(0^2)-7(0)+c = 8 \\c=8$

This gives you your function to be

$\frac{5}{3}x^3+\frac{9}{2}x^2-7x+8$