Lindsey's Reflection

this week we started chapter 3.
the first thing we learned about was
finding extremas and max and mins.

there are steps to doing so.
here they are:

step1:

take the derivative and set it equal to zero.
solve for x.

step2:

find any place the function
is not differentiable.

step3:

plug in to get a y value
if asking about a max
or a min specifically.

step4:

if on an interval plug
in to get a y value for
each.

step5:

the highest is the max
the lowest is the min.

if you are looking to find an extrema
the first two steps are all you need to
use. but in order to find and max and a
min you have to use all five steps.

here is an example:

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

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

2. ok

3. f(0)=0
f(1)=-1-min

4. f(-1)= 7
f(2)=16-max


thats all there is to it and if you
were just looking for the extrema
like i said all you would look
at is the first two steps and in
this case the extrema or critical numbers
would be 0 and 1.

goodnight.