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Let f(x) = sin x + cos x on [0, π/2]. Check that the ends have equal values, and find the point c…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Let $f(x) = \sin x + \cos x$ on $\left[0, \dfrac{\pi}{2}\right]$ . Check that the ends have equal values, and find the point $c$ promised by Rolle's theorem, to four decimal places.

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

Have you tried it?

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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