Chapter 4 - Section 4.2 - The Mean Value Theorem - 4.2 Exercises - Page 292: 32

$f(x) = cx+d~~$ for some constant $d$

Let $g(x) =cx$ Then $g'(x) = c$ $f'(x) = g'(x) = c~~~~$ for all $x$ According to Corollary 7, $f(x) = g(x)+d$ for some constant $d$ Thus, $f(x) = g(x)+d = cx+d~~$ for some constant $d$