Answer to Question #115491 in Real Analysis for noof

Question

If f0(x) = c (c a constant) for all x, to show f(x) = cx + d (Do not use integration)

Answer 1

Given f'(x)=c

Consider g(x)=f(x)−cx. Then g'(x)=f'(x)−c=c−c=0.

Therefore g is constant, say g(x)=d.

Then f(x)=cx+d.