Lindsey's Reflection

So i forgot to do my first blog but here's my second.

since we were off we didnt do anything new
so this blog is going to be about the first derivative test.

here are the steps to this process:

1. take the derivative. set it equal to zero.

2. find anywhere that it is not differentiable.

3. set up intervals using the first two steps of the
process.

4. plug in a number from each interval you
found into the derivative equation.

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

6. determine the max or min from
step 5
increasing- max
decreasing-min

here an example:

find the relative extrema of
f(x)=(x^2-4)^2/3

1. 2/3(x^2-4)^-1/3(2x)=0

4x/3(x^2-4)^1/3=0

4x=0

x=0

2. x^2-4=0
critical point=-2,0,2

3. (-infinity,-2)u(-2,0)u(0,2)u(2,infinity)

4. f^1(-3)=-ve-dec
f^1(-1)=+ve-inc
f^1(1)=-ve-dec
f^1(3)=+ve-inc

max: x=0

min: x=-2,2

thats all to it. see everyone tomorrow.