First reflection on the 2nd semester

So this week we took it pretty easy we just reviewed some stuff. One of the things we reviewed was the first derivative test……an that’s what this blog’s on.
STEPS:

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