# Rate of Change and Derivatives Applied to a Falling Rock and Profit Margin

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A rock is dropped from a tower on the Brooklyn Bridge, 276 feet above the east river. Let t represent the time in seconds.

a.) write a model for the position of the function (assume air resistance is negligible.)

b.) find the average velocity during the first 2 seconds.

c.) find the instantious velocity when t=2 and t=3

d.) how long will it take before the rock hits the water ?

e.) when it hits the water, what is the rock's speed?

Find the marginal profit function

P= -0.0002x^3 + 6x^2 - x - 2000

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Rate of change and derivatives are applied to a falling rock and to profit margin. The solution is detailed and well presented.

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