Lindsey's Reflection

This week we just reviewed
the first derivative test and the
second derivative test.

here is the steps to the first derivative
test:

1. take derivative and set it equal to
zero.

2. find anywhere it is not differentiable

3. set up intervals using the first two steps.

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

5. if it is positive it is increasing if
it is negative it is decreasing

6. determine which is the max and which is
the min using step five

increasing- max
decline-min

here are the steps for the second derivative
test:

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

2. find anywhere it is not differentiable

3. set up intervals using steps one and
two

4. plug in a number on the interval into
the 2nd derivative equation

5. if it is positive it is concave up and if
it is negative it is concave down

6. if changes from + to - or - to +
there is a point of inflection.

We also learned the shortcut to the
first derivative test this week:

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

2. take the second derivative.

3. plug in x values from step 1.
-if positive- min
-if negative-max

**the test fails if there is no second
derivative

here is an example using the shortcut:

3x^5+5x^3

1. -15x^4+15x^2=0
15x^2(-x^2+1)=0

x=0, +/- 1

2. -60x^3+30

f(0)=0 --the test fails
f(1)=- max
f(-1)=+-min