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## Derivative Review Problems

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**Wouldn’t it be great if everybody in the world lightened**up? Ignore the occasional low Calculus grade Why can’t we Get along? Live and Let live Always wait for the context Let bygones Be bygones**Calculus 2413**Chapter 3(10) Related Rates**When a pool is filled the change in the depth is related to**the change in the volume. You might consider When a ladder leans against a building and the bottom (x) is moved away from the building the top (y) will move down. You might consider Related Rates Used when you have change related to time**Related Rates - Steps**• Draw a picture and find or write an equation relating two variables. 2) Take a time derivative of the equation. 3) Put in values that you know and solve for what you are missing.**Example 1: Find the rate of change in the distance**between the origin and a moving point on the graph of:**Example 2:**The diameter of a circle is increasing at a rate of 4 ft/sec. How fast is the area increasing when the diameter is 10?**Example 3:**Water is being poured into an inverted cone at a rate of 10 ft3/sec. At the top, the radius of the cone is 8 and the depth is 20 feet. How fast is the depth rising when the water is 7 feet deep?**A 30 ft. ladder is leaning against a building and the bottom**is pulled out at a rate of 3 ft/min. How fast is the top of the ladder moving down when the bottom is 12 ft. from the building? Example 4: 27.5 12