Here are initial hints for Quiz 4 problems:

1. For this problem you need to remember that velocity is the first derivative of the position function x(t) with respect to time.

2. The formula describing f(x) is in quadratic form. If you use substitution z=x^2, you will have easier time seeing how to factor it. Once you have factored f(x) review how to solve polynomial inequalities.

3. Apply the method for solving polynomial inequalities you used in #2.

4. First find the slope of the given line. Then find the point on the given curve such that the tangent line at that point has the same slope. Then you should be able to find k.

5. Find the derivative of both formulas at x=2 and then make the derivatives equal to find c+d

6. This problem requires you to discover the relationship between the derivative of a function and the derivative of its inverse function. I suggest you first check what happens for lines (i.e. what is the relation for slopes of lines which are inverses of each other. Then draw some pictures of inverse functions and their tangents: x^2 and sqrt(x); lnx and e^x. Lastly apply your findings to the problem.  

posted 10/7/2010 2:42 PM | comment | view comments (0)