What are related rates?
Using derivatives to calculate unknown quantities in relation to other quantities and their rates of change.
What quantity is typically related to other quantities in related rates problems?
Time.
Steps to solve related rates problems?
1. Identify knowns and unknowns. 2. Establish a relationship (equation). 3. Differentiate w.r.t. time. 4. Substitute and solve.
How to approach a related rates problem involving a circle's area?
1. Identify $\frac{dr}{dt}$ and $r$. 2. Use $A = \pi r^2$. 3. Find $\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$. 4. Substitute and solve.
How to approach a 'ladder' related rates problem?
1. Draw a diagram. 2. Use $x^2 + y^2 = L^2$. 3. Differentiate. 4. Substitute knowns and solve for the unknown rate.
What is the area of a circle?
$A = \pi r^2$
What is the Pythagorean Theorem?
$a^2 + b^2 = c^2$
