Question

Find two possible functions f, given the second-order
derivative.
f "(x)=x²+ 8

Answer 1

To find two possible functions f given the second-order derivative, integrate the derivative twice. The first-order derivative of f will be (1/3)x^3 + 8x + c1, and the function f will be (1/12)x^4 + 4x^2 + c1x + c2 after integrating the first-order derivative with respect to x.

Step-by-step explanation:

Given the second-order derivative, we can find two possible functions f by integrating the derivative twice. First, integrate x^2+8 with respect to x to find the first-order derivative of f: f'(x) = (1/3)x^3 + 8x + c1. Then, integrate f'(x) with respect to x to find f(x): f(x) = (1/12)x^4 + 4x^2 + c1x + c2, where c1 and c2 are constants of integration.