Question

How do you find the value of values of c that satisfy the equation [f(b)-f(a)]/(b-a) in the conclusion of the Mean Value Theorem for the function `f(x)=x^2+2x+2` on the interval [-2,1]?

Answer 1

First, find `f'(c)=2c+2`. Next, find `(f(b)-f(a))/(b-a)=(f(1)-f(-2))/(1-(-2))=(5-2)/3=1`. Now set `2c+2=1` and solve for `c` to get `c=-1/2`.