Math 161

Sample First Midterm

Problem 4b

Dr. Wilson

4b. Find the first and second derivative.

To get the first derivative, we use the quotient rule

For the second derivative, we use the quotient rule again.

Unlike polynomials, the more you differentiate a rational function, the more complicated it gets. We can simplify it somewhat by noticing that each of the terms in the top has at least one factor of x2 - 4x + 3.

This factor of x2 - 4x + 3 in the top will cancel one of the 4 factors in the bottom.