# Thread: Is the function f(x) differentiable?

1. ## Is the function f(x) differentiable?

Please explain.

2. Do you know the sufficient and necessary conditions for a function to be differentiable?

3. Originally Posted by acarril2

Please explain.
Use first principles e.g

$\displaystyle \displaystyle \lim_{x \to 0}\frac{f(x)-f(0)}{x-0}$

Hint: the squeeze theorem will be helpful.

4. 1) Use the usual rules of differentiation to find the derivative for x NOT equal to 0.

2) Use $\displaystyle \lim_{h\to 0} \frac{f(h)- f(0)}{h}$ to find the derivative AT x= 0.

This problem does NOT ask if the derivative is continuous at x= 0 so it is not necessary to show that the limit of (1), as x goes to 0, is the same as (2), as I first wrote. (But you might find it interesting to do so.)