Question

Let f(x) = tan(x). Show that f(0) = f(pi) but there is no number c in (0, pi) such that f'(x) = 0. Why does this contradict Rolle's Theorem?

Answer 1

Rolle's theorem is telling you three things that have to be true about a given function f(x). 1. f(x) is continuous on [a,b]. 2. f(x) is differentiable on (a,b). And 3. There is a number c within (a,b) such that f'(c) = 0. SO, which part of Rolle's theorem does that violate?

What you do to solve this is verify that f(x) = tan(x) will equal zero when you plug in 0 and pi for x. If f(x) does equal zero for each x value of 0 and pi, then you can do the next step. Next, you differentiate f(x), you should know the derivative of tan(x) is sec^2x or (secx)^2. If (secx)^2 = 0 for any x between (0,pi) then Rolle's theorem is valid. If not, then Rolle's theorem does not apply.

Answer 2

Do you have any questions about what I told you or does that make sense?

Answer 3

It makes sense, thank you

Answer 4

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