Chapter 4: Applications of Derivatives - Section 4.2 - The Mean Value Theorem - Exercises 4.2 - Page 198: 31

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

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