In order to show that a function satisfies the mean value theorem on a particular interval, we'll use the mean value theorem formula. In order to use the formula, we have to know first that the function is both continuous and differentiable on the interval. If the function meets these two conditions, then we can apply the mean value theorem formula.
In order to find the value of c where the function has its mean value in the interval, we have to find the value of the function at the interval's endpoints. We'll also find the derivative of the function at the point c.
Once we have all of this, we'll plug everything into the mean value theorem formula, and that'll allow us to solve for the value of c that corresponds to the mean value of the function in the interval.
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