Chapter 4 - Section 4.2 - The Mean Value Theorem - Exercises - Page 223: 36

a) $y=\sqrt x+C$ b) $y=2 \sqrt x+C$ c) $y=2x^2-2\sqrt x+C$

a) When $(\sqrt x)'=\dfrac{1}{2 \sqrt x}$ Thus, $y'=\dfrac{1}{2 \sqrt x}\implies y=\sqrt x+C$ b) When $( 2\sqrt x)'=\dfrac{1}{ \sqrt x}$ Thus, $y'=\dfrac{1}{\sqrt x}\implies y=2 \sqrt x+C$ c) When $( 2x^2-2\sqrt x)'=4x-\dfrac{1}{ \sqrt x}$ Thus, $y'=4x-\dfrac{1}{ \sqrt x} \implies y=2x^2-2\sqrt x+C$