Caculus Corollary 7 problem?

Question

Suppose c is a constant such that, for all x, f prime x is equal to c. Use Corollary 7 to prove that there is a constant such that f(x) = cx + d for all x. Let g(x) denote the function c x.

Corollary 7: If f prime x = g prime x for all x in an interval (a,b), then f - g is constant on (a,b); that is, f(x) = g(x) + c where c is constant.

Answer 1

You're practically given the answer here: Let g(x) = cx, then ∀x, f'(x) = c = g'(x), so f-g is constant, so f(x) = g(x) + d = cx + d for some constant d.