# Falling Ladder: Related Rates Question

- Author:
- Gail Neal, Tim Brzezinski

Question (1) taken from Stewart's Calculus (Early Trancendentals) text:
1) If

**the ladder is moving away from the wall at 1 ft/sec**,**how fast is h changing at the exact instant when x = 6 ft?**2) Why is dh/dt < 0 (regardless of the point at which the ladder meets the floor)? Explain. 3) At what instance does the absolute value of dh/dt the greatest? How is this made apparent? 4) At what instance does the absolute value of dh/dt the least? How is this made apparent? 5) Is there ever a time for which the absolute value of dx/dt = the absolute value of dh/dt? If not, explain why. If so, determine the values of h and x for which this occurs.