Chapter 4 - Section 4.2 - The Mean Value Theorem - Exercises - Page 223: 33

a) $y=\dfrac{x^2}{2}+C$ b) $y=\dfrac{x^3}{3}+C$ c) $y=\dfrac{x^4}{4}+C$

a) When $x=(\dfrac{x^2}{2})'$ Thus, $y'=x \implies y=\dfrac{x^2}{2}+C$ b) When $x=(\dfrac{x^3}{3})'$ Thus, $y'=x^2 \implies y=\dfrac{x^3}{3}+C$ c) When $x=(\dfrac{x^4}{4})'$ Thus, $y'=x^3 \implies y=\dfrac{x^4}{4}+C$