Blog 10

Happy Halloween! :)

Anyways, We just finished chapter three which was all the guidelines stuff. It was pretty easy but just like every other chapter they had parts that were very confusing. For me the confusing stuff was the problems that dealt with trig. I still don’t understand the whole quadrant thing; I just forgot it from last year. But something I do remember was the two theorems and I’ll explain them since I didn’t get to last blog. So, the two theorems are Rolle’s Theorem and Mean Value theorem. The confusing part is that they both deal with max’s and min’s. Here are some hints to tell them apart: Rolle’s Theorem only applies to questions on an interval, and it tells you that there is at least one max or min, however there could be more than one. Now to find out if the number is on the interval, you’re going to take the derivative and set it equal to zero. If the number is in the interval then you would plug it back into the original equation to see if it is a max or min. **Typically Rolle’s Theorem uses x-intercepts. The Mean Value Theorem deals with slope. You set the slope equal to the derivative and solve to find the number in-between.

EXAMPLE OF ROLLE’S THEOREM:
Ex. 1: Find the 2x-intercepts of f(x)=x^2-3x+2 and show that f’(x)=0 at some point between the 2x-intercepts.
*Check if continuous-It’s continuous
*Check if differentiable-Yes
*Solve for 0 to find interval
X^2-3x+2=0
(x-2)(x-1)=0
X=1,2 [1,2]

EXAMPLE OF MEAN VALUE THEOREM:
Ex. 2: Given f(x)=5-(4/x) find all values of c in the open interval (1,4) such that f’(c)=f(4)-f(1)/4-1
*Continuous
*Differentiable
*Set slope=derivative
4=x^2
X=+/- 2