Question

How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function `f(x)=x^2 - 2x + 5` on the interval `[1, 3]`?

Answer 1

Solve `2x-2=2`

Explanation:

One way to write the conclusion of the Mean Value Theorem for the function `f(x)` on the interval `[a, b]` is:

There is a `c in (a,b)` such that `f'(c) = (f(b)-f(a))/(b-a)`.

In this question, we have `f(x)=x^2 - 2x + 5` on the interval `[1, 3]`

So, find `f'(x)`.
Find `(f(3)-f(1))/(3-1)`.
Set them equal to one another and solve the resulting equation.
If the equation has more than 1 solution, list only the solutions in the interval `(1,3)`.