Method: Mean Value Theorem for Definite Integrals

Step 1: Determine the Average Value, $f_{\mathit{avg}}$, of your given equation, $f\left(x\right)$, over the given the x-interval , [ a , b ] using the Average Value formula.

Step 2: Set your given equation, $f\left(x\right)$, equal to the average value you found in Step 1 , $f_{\mathit{avg}}$, and solve for x (i.e., get x alone on side of the equals).

Any of those x-values that are inside the given x-interval , [ a , b ], is a c-value that the Mean Value Theorem for Definite Integrals guarantees you that you would find.