Question

Give two examples, graphical or algebraic, of differentiable functions. Explain why they are differentiable.

Answer 1

@zepdrix can u help?

Answer 2

Hmm so by differentiable, I guess they mean ~ A function who's derivative `exists` over it's entire domain.

Here's an example of a function which is NOT differentiable,\[\large f(x)=|x|\]Remember this function? It's the one that looks like a V shape.
If we plug in \(x=0\), we can see that the function IS defined there, a value exists.
But if we take the derivative of this function, no such derivative will exist at \(x=0\) because there is a discontinuity there.

Answer 3

It's actually harder to come up with non-differentiable functions lol :) It's funny that they asked this question in the way that they did.

Answer 4

Here is one differentiable function.\[\large f(x)=x^2\]
The domain is all real numbers (as was the case with absolute x), but if we take the derivative of this function, the derivative exists at ALL POINTS.

Answer 5

The derivative exists over the entire domain*

Can you think of another function? :)

Answer 6

okay so its asking for differentiable and non- differentiable

Answer 7

Ok so we have one example of each so far. Do you need 2 examples of each type?

Answer 8

no only one

Answer 9

you can chose between graphical or algebraic

Answer 10

So I was giving examples algebraically.
If you wanted to show it graphically, here is what the absolute function would look like.

Answer 11

okay this one is for non-differentiable right?

Answer 12

I'm not sure if you need this, but here is what the derivative looks like. Just in case it helps.

Yes the non-differentiable. It's not differentiable at a point along the function.

Answer 13

okay thanks