Let "f" be a function defined everywhere on the real axis, with a derivative f ' which satisfies

(cont'd) the equation : f ' (x) = c * f(x) for every x, where 'c' is a constant. Prove that there is a constant K such that f(x) = K*e^(cx) for every x. [ Hint : Let g(x) = f(x)e^(-cx) and consider g ' (x)]