Calc BC Pham Unit 4

How do you solve related rates problems?

• Identify the rates, relationship, and moment

• Differentiate relationship wrt time (implicitly)

• Plug in knowns to solve for unknown rate

How do you solve optimization problems?

• Find primary and secondary equations

  • Primary equation: equation to minimize/maximize

  • Secondary equation: relationship btw variables

• Use secondary equation to write primary equation in terms of one variable

• Differentiate and find critical points

• Do candidacy test (if multiple critical points)

• Ensure that the points you find answer the question

What is the volume of a prism?

What is the volume of a cylinder?

What is the volume of a cone?

What is the volume of a sphere?

What are absolute extrema?

The highest and lowest points of a graph on an interval

How do you find absolute extrema?

• Differentiate the function

• Find where f’(x)=0 or undefined on the interval

• Make a candidacy chart (shown below)

• Points with highest magnitude are absolute minima/maxima