Example from section 3.4

1. A 12 foot long ladder rests against a vertical wall. Let be the angle between the top of the ladder and the wall and x be the distance from the wall to the bottom of the ladder. If the bottom of the ladder slips away from the wall, how fast does x change with respect to when ?

Steps to solving an application problem asking for a rate:

1. Draw a picture and label the picture.

2. What are you looking for? (What do you want?)

3. Come up with a relationship between the variables (Relate known and unknown).

4. Differentiate both sides of the equation/relationship.

5. Plug in the given value of the angle to determine the rate of change at the given instant. (Substitute and solve)