holiday blog 3

in this blog i will go over stuff we did right before the holiday, well kinda before the holidays, im more refreshing the first derivative test cause i know we will be asked this and i want to BAM knock her dead with my answer!
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
x/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