Assume that f and g are differentiable functions defined on all of the real line. It is possible that everywhere, everywhere, and everywhere.

Question

Assume that f and g are differentiable functions defined on all of the real line. It is possible that  everywhere,  everywhere, and  everywhere.

Quizplus · Accepted Answer

If f(x) and g(x) are both differentiable functions and their derivatives are always equal, then f(x) and g(x) differ by at most a constant. Therefore, it is not possible for f(x) and g(x) to be different functions with equal derivatives everywhere.

Assume That F and G Are Differentiable Functions Defined on All