Скачать или смотреть Related Rates – Ladder Sliding Down a Wall

This example of a standard related-rates exercise in Calculus is of a ladder sliding down a wall at a constant rate. We are asked to determine the length of the ladder given the speed of the ladder’s base sliding away from the wall at a specific time. We follow the steps to solve related rates problems, which are common in Calculus:

1. Read and re-read the problem to gain an intuitive understanding. Sketch a diagram, if possible. Identify rates that are given and the rate that is to be determined.
2. Write an equation that relates the various quantities of the exercise. If necessary, use geometry to eliminate a variable.
3. Use the Chain Rule to differentiate both sides with respect to t.
4. Substitute known values and solve for the desired quantity.
5. Check that the answer is reasonable.

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