Differentiables

Hey guise, its me Not Paul making my blog post for today because I'm Not* Scribe.
*Truthiness may vary

Anyway, onto actual Mathematics, those darn derivative deriving derivates and what in the heck a differentiable function is. I cannot however tell you with absolute certainty what a differential is, but I have a good idea we're going to find out soon enough.

The basic definition of a differentiable is a function where the derivative can be found for any point of a defined segment of that function.

Which is why f(x) = x^2 is differentiable, because we can find the derivative for every point in the function or any portion of the function.

If you get a function with "kinks" or very pointy points when you graph it, it won't have derivatives at those pointy points and thus is not differentiable for the entire function.

However, if you define a segment of that function that doesn't have pointy points then you can say that the function is differentiable for this segment of the function.

The teacher's definition is as follows:

"A function (fcn) is said to be differentiable at variable a if at variable a f '(a) exists. It is called differentiable on an interval if it is differentiable for every number in the interval."


Here's the example from yesterday that we did today [Ex 1] (which we also did yesterday), and another example we did [Ex 2]. Both of these are differentiable, because the derivative f '(x) exists at x = 0. (in Example 1 replace variable a with x)

Ex 1)


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Ex 2)


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This is an example where f '(0) doesn't exist, therefore it is not differentiable.

Ex 3)



(Click to view larger)

As shown in the image, the function f(x) = |x| is not differentiable because when x = 0, its derivative does not exist/cannot be determined tangentially. If graphed, y = |x| would show it has a "kink" or pointy point at x=0.

At the end of class we started talking about the different people who invented Calculus, and importantly Joseph Louis Lagrange's contribution of f '(x) = dy/dx, which will come up later in the course I'm sure of it, because of this Wikipedia article.

The next scribe shall be...

Zeff (zeph)

Sorry this post is uncredibly late, you can blame Wired and NeoGAF for their unfairly up-to-date news. I started working on this post at 9pm and finished 4 hours later. Of course atleast one of those hours was spent trying to figure out OpenOffice...