- #1
skyturnred
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Homework Statement
I am trying to prove that f(x)=x[itex]^{4}[/itex]-x-1 has exactly one root on [1,2].
Homework Equations
The Attempt at a Solution
Step one, by intermediate value theorem I proved that there is at least one root on [1,2]. But I don't know how to go about proving there is only that single root. We were taught how to do this with Rolle's Theorem, but since this does not satisfy the conditions for Rolle's Theorem, I can't use it.
I think that I must somehow use the mean value theorem.. But I don't know how.