Chapter 4 - Section 4.2 - The Mean Value Theorem - Exercises - Page 223: 31

a) 4, b) 3, c) 3

We have $f(x)= x^2+c$ and $f'(x)=2x$ a) $f(0)=0 \implies 0=0^2+c \implies c=0$ and $f(2)= 2^2+0=4$ b) $f(1)=0 \implies 0=1^2+c \implies c=-1$ and $f(2)= 2^2-1=3$ c) $f(-2)=3 \implies 3=(-2)^2+c \implies c=-1$ and $f(2)= (2)^2-1=3$ Hence, a) 4, b) 3, c) 3