Question

Find f. f '(x) = x-2, x > 0, f(1) = 0, f(5) = 0?

Answer 1

To find f, we need to integrate f'(x) = x-2 and solve for the constant of integration using the given function values. The specific function f(x) can be found by substituting the values f(1) = 0 and f(5) = 0.

Step-by-step explanation:

To find f, we need to integrate f'(x). Since f'(x) = x-2, we can integrate both sides with respect to x:

∫f'(x) dx = ∫(x-2) dx

Integrating, we get f(x) = &frac;1&frac;2x^2 - 2x + C, where C is the constant of integration. Given that f(1) = 0 and f(5) = 0, we can substitute these values to solve for the constant and find the specific function f(x).