2.8 Derivatives

No, I am not Isabella because she relinquished her possesion of this section to me, Laurie. So, TESSA, you are next.

In previous lessons, we have learned that

the slope of the tangent line = instantaneous rate of change = derivative

The 2 equations to reach any of these three values are:
lim f(x) – f(a)/(x – a)
x->a
lim f(a+h) – f(a)/ (h)
h->0

Lesson 2.8 simply teaches us a way to restate these long equations with

"f prime a", which would be represented with f ' a.

Which is a less arduous way to express a problem. (Though why they had an entire lesson on it, I cannot fathom. =] Good for me.)

Sample Problem:
Provided that f(x) = x^2, what is f ' 1?

1) (x^2-1)/(x-1)
2)(x+1)(x-1)/(x-1)
3) cancel the (x-1)
4) = x+1
5) 1+1 = 2

Here is a site that can help you better understand the derivative.
http://en.wikipedia.org/wiki/Derivative

Remember on Sesame Street when Ernie would sing Rubber Ducky? I personally think that this rubber ducky is much cuter.