Chapter 4: Applications of Derivatives - Section 4.2 - The Mean Value Theorem - Exercises 4.2 - Page 198: 32

$a) y=x^2+C; b) y=x^2-x+C; c) y=x^3+x^2-x+C$

a) When $2x=(x^2)'$ This implies, $y'=2x$ and $y=x^2+C$ b) When $(2x-1)=(x^2-x)'$ This implies, $y'=2x-1$ and $y=x^2-x+C$ c) When $(3x^2+2x-1)=(x^3+x^2-x)'$ This implies, $y'=(x^2+x-x)$ and $y=(x^3+x^2-x+C)$