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Let f(x) = x² - 6x + 8 on the interval [2, 4]…

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Let $f(x) = x^2 - 6x + 8$ on the interval $[2, 4]$ . Find $f(2)$ and $f(4)$ , and find the point $c$ in $(2, 4)$ given by Rolle's theorem.

Need a reminder? The key ideaShow

Rolle's theorem: if $f$ is continuous on $[a, b]$ , differentiable on $(a, b)$ and $f(a) = f(b)$ , then $f'(c) = 0$ for some $c$ in $(a, b)$ . Check all three conditions, then solve $f'(c) = 0$ and keep the solutions inside $(a, b)$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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