How do you find a number c that satisfies the conclusion of the theorem for the function f(x) = x^2 - 3x + 1f(x)=x23x+1 on the interval [-1,1]?

1 Answer
Sep 12, 2015

cc is a solution to the equation f'(x) = (f(1)-f(-1))/(1-(-1))

Explanation:

For f(x) = x^2 - 3x + 1 on the interval [-1,1]

We get:

f'(x) = (f(1)-f(-1))/(1-(-1))

2x-3 = ((-1)-(5))/(1-(-1)) = (-6)/2 = -3

So x=0

This is the only solution and is, of course in the interval mentioned in the conclusion of MVT. That is, it is in (-1,1).

So the c we want is c=0.