# j-james/math

All my math notes, now in Markdown.

View the Project on GitHub j-james/math

# 4-6 Related Rates

## Learning Targets

You will be able to

• Solve application problems involving multiple rates

## Concepts / Definitions

Solve related rate problems like any other story problem.
These problems often involve implicit differentiation because the questions involve problems asking for a rate of change with respect to a variable different than the variables in the equation.

Important

1. Do not substitute given values unless it remains constant in the problem.
2. Don’t forget rule #1.

If you have a ladder leaning against the side of a building, and the bottom is sliding out at a constant 3ft/sec, does the bottom slide down at a constant?
No, it doesn’t. It slides slower at first, then faster at the bottom.

A 50 foot ladder is placed against a building. The base of the ladder is resting on an oil spill, and it slips at a constant rate of 3 feet per second. Find how fast the top of the ladder is sliding down at the instant when the base of the ladder is 30 feet from the base of the building.

Our one constant value is the length of the ladder, always staying at 50. Knowing this and knowing that the ladder forms a right triangle with the wall, we can establish the equation $x^2 + y^2 = 50^2$.

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