# Squeeze Theorem for derivatives

#### benf.stokes

1. The problem statement, all variables and given/known data

Show, with appropriate examples, that the conditions g(x) < f(x) < h(x) and derivative(g(x0))=derivative(h(x0)) = m does not imply derivative(f(x0)) = m or even exists. And with some additional condition.

2. Relevant equations

derivative g(x) = lim(h tends to zero) (g(x+h)-g(x))/h

3. The attempt at a solution

How do I even get started?
Thanks

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#### jbunniii

Homework Helper
Gold Member
Start by identifying the simplest function you can think of which has no derivative at, say, x = 0.

By the way, the problem seems almost too simple as stated. But what do you mean "and some additional condition"? Are there some more constraints on g, f, and/or h? E.g., do their values have to be close to each other at $x_0$?

#### benf.stokes

Thanks for the reply. The problem does require a formal proof although I know it may not appear because of my sloppy translation.
And the aditional conditional means that something other than g < f < h is required for deriv g < deriv f = deriv h = m

"Squeeze Theorem for derivatives"

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