post 36

calculussssssssss


Optimization:
1. Identify all quantities
2. Write an equation
3. Reduce equation
4. Determine domain of equation
5. Determine max/min values

Finding absolute max/min:
1. First derivative test
2. Plug critical values into the original function to get y-values
3. Plug endpoints into the original function to get y-values
4. The highest y-value is the absolute maximum
5. The lowest y-value is the absolute minimum

Volume by disks:
Pi bSa [R(x)]^2 dx

Volume by washers:
pi bSa (top equation)^2 – (bottom equation)^2 dx

Limit Rules:

1. if the degree of the top is bigger than the degree of the bottom, the limit is infinity.

2. if the degree of the top is smaller than the degree of the bottom, the limit is 0.

3. if the degree of the top is equal to the degree of the bottom, the limit is the coefficient of the leading term of the top divided by the coefficient of the leading term of the bottom equation.

First derivative test:
-Take the derivative of the original function
-Solve for x (the values will be your critical values)
-Set those values up into intervals between negative infinity and infinity
- Plug in numbers between the intervals into the function
-This will show you when the function is increasing, decreasing, and you will find max's and mins

Second derivative test:
-Take the derivative of the original function twice
-Solve for x values(critical values)
-Set up into intervals between infinity and negative infinity
-Plug in values between the intervals into the function
-This will show you where the graph is concave up and down, and where there is a point of inflection.

i am not good at some integrals and ooptimization.