Halloween Blog of the Dead - topsgolbredrum

This week went by pretty fast, although not one of the best weeks. Pretty tired, almost killed myself nd my parents in a car crash yesterday, sleepin at the wheel, tsk tsk. ANWAYS, to the math, i guess. We didn't learn much this week, except for continuing blah blah in chapter 3 and goin back to chapters 1 and 2. I guess i'll explain how to do some more fricking derivative, using the Mean Value Theorem.

First, you have to check if the function is continuous or not. If it is, move to step 2.

Second, you have to check if the function is differentiable or not. If it is, move to step 3.

Third, you have to do something with the slope.

Use the function

f ' (c) = (f(b) - f(a))/(b-a)

It means on an interval [a,b]. There must be some x-value where the derivative equals the slope between a & b.

slope of a secant line = slope of a tangent line between a & b.

Example:

Given f(x) = 5 - (4/x), find all the values of c in the open interval (1,4) such that

f ' (c) = (f(4) - f(1))/(4-1)

1. continuous? yes

2. differentiable? yes

4-1/4-1 = 3

5 - 4x^-1

4/x^2 = 1

4 = x^2

x = plus or minus 2

c = plus or minus 2

By the mean value theorem, the function is continuous and differentiable, therefore the same value c=2 where f ' (x) = the slope between the open interval (1,4).