1. The Parks Department is monitoring the water level of a lake. The change in water level of the lake is modeled by a third degree polynomial function, P(x).

A) What do the x-values when P(x) = 0 tell you about the real world situation?

B) Explain how you would find those x-values for which P(x) = 0. State the theorems or procedures covered in this unit that you could use to help you find those x-values.

2.In your lab, a substance's temperature has been observed to follow the function f(x) = (x ? 1)³+ 9. The point at which the function changes curvature from concave down to concave up is where the substance changes from a solid to a liquid. What is the point where this function changes curvature from concave down to concave up?

Hint: The point is labeled in the picture.

3.Two students in your class, Jim and Mike, are disputing a function. Jim says that for the function, between x = ?1 and x = 1, the average rate of change is 0. Mike says that for the function, between x = ?1 and x = 1, the graph goes up through a turning point, and then back down. Explain how Jim and Mike can both be correct, using complete sentences.

4.You are having a conference call with Mr. Smith who is the owner of a paper company. You have interpreted the number of trees cut down versus profit as the following function.

T(x) = ?x⁴+ 3x³+ 21x²? 43x ? 60

For what numbers of cut trees will the company break even? Show the work steps to determine these numbers.

Hint: The company will break even where T(x) = 0.

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