Question

Determine if the following statement is true or false.



(c) If f '(x) = g '(x) for all x in (a, b), then there is a constant K such that f(x) = g(x) + K on (a, b).

Answer 1

true. taking the derivative drops the constant.

here is an example
\[f(x)=2x\qquad g(x)=2x+2\]\[f'(x)=2=g'(x)\]