Chapter 4: Applications of Derivatives - Section 4.2 - The Mean Value Theorem - Exercises 4.2 - Page 198: 29

$a) 4, b) 3, c) 3$

Given: $f(x)= x^2+c$ This implies $f'(x)=2x$ a) $f(0)=0$ and $0=0^2+c \implies c=0$ ; $f(2)=( 2)^2+0=4$ b) $f(1)=0$ and $0=1^2+c \implies c=-1$; $f(2)= (2)^2-1=4-1=3$ c) $f(-2)=3$ and $3=(-2)^2+c \implies c=-1$ ; $f(2)= 2^2-1=4-1=3$