Math 121 take home

1. The slope of the tangent line for a function at is defined to be

1. If use and respectively to approximate

2. If use and respectively to approximate

2. Find a profit function satisfies the following conditions, where denotes number of units are produced and is a polynomial function: (a) the company breaks even at and units (b) the profit function changes signs (from to or vise versa) at but does not change sign at and (c) the company is NOT profitable when units are produced.

3. Sketch the function above.

4. Let

1. Sketch

2. Find the function so that the graph of is being shifted to the left units and down units from

3. Find the inverse function for and graph the inverse function together with

5. Let be the function graphed below:

1. Does have an inverse in the domain of Explain.

2. If we restrict the domain of to be does exist? Explain.

3. If and find and

6. If If

1. Sketch the graph of

2. Find

3. Find

7. If

1. Sketch the graph of

2. Find

3. Find