Justin 8

This week we wrapped up chapter 2 and went into chapter 3

what we learned so far is sort of a repeat of ch 2, finding extrema

THE RULES:
1. Find the critical numbers
2.Evaluate at each critical number
3.Evaluate at each endpoint
4.The least of the values is the min. the greatest is the max
5.Anything not differentiable is a critical number

we work out problems in this chapter by looking at graphs (sometimes)

the absolute max is the highest point on the interval
the absolute min is the opposite (duh)
the relative max is any max that is not on the interval
the relative min is any min '' '' ''
a critical number is any max or min typically referred to as x=c

Find the extrema of f(x)=3x^4 - 4x^3 on the interval [-1,2]

12x^3 - 12x^2 = 0
12x^2 (x-1)=0
x=0,1

To determine max/min on an interval
f(-1)=7
f(0)=0
f(1)=-1 absolute min
f(2)=16 absolute max