Lindsey's Reflection

So we have a test tomorrow.
im super nervous but this is what
its on!

Steps for finding extremas, maxs, or mins:

1. take a derivative and set it equal to zero.

2. find any place the function is not
differentiable.

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

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

5. the highest number is the max.
the lowest number is the min.

if you are looking for just extrema then only
use the first two steps but if you are looking
for max and min you have to use every
step.

Roolle's Theorem:

1. make sure it is continuous.

2. make sure it is differentiable.

3. make sure that the y values match.

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

you use roolle's theorem when trying to find
a max or min or when you are trying to prove
there is a max or a min.

Mean Value Theorem:

-set derivative equal to slope
between 2 points and there has to be
a value x. you can solve for it if it is continuous and
differentiable on the interval.

First Derivative Test:

1. take derivative and set it equal to zero.

2. find anywhere it is not differentiable

3. set up intervals using steps 1 and 2.

4. plug in a number on the interval into the derivative equation

5. if +ve it is increasing. if it is -ve it is decreasing

6. determine max or mins.

increasing- max

decreasing- min