I have this problem, f(x) = (√x) - 2x On some interval [0,1].(adsbygoogle = window.adsbygoogle || []).push({});

One of the things im supposed to do is to show that it's differentiable on the interval.

Now, I am aware that the definition of the derivative is f'(x) = lim as h[itex]\rightarrow[/itex] 0 of [itex]\frac{f(x+h) - f(x)}{h}[/itex] and that this formula is used to produce the derivative function of f(x).

And that replacing the x with a known x value into the formal definition should produce a derivative value at given x value.. so that using this definition of the derivative would tell me whether or not a function ata single x valueis differentiable.

First Question, is what I said thus far correct?

Given what I said above is correct,

I don't want to find the derivative of f(x) = (√x) - 2x at any one single value. I want to find whether or not it is differentiable on the interval [0,1].

How does the formula lim as x→[itex]x_{0}[/itex] of f(x) - f([itex]x_{0}[/itex])/ x - [itex]x_{0}[/itex] come into play and how does it relate to the above definition of a derivative formula?

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# [(f(x+h) - f(x))/h] versus [(f(x) - f(0))/x]

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