Quiz 8

Date: MATH 1210-4 - Spring 2004

Note: Unless stated otherwise, answers without justification receive no credit. Please, show your work!

1. Let $g(x)=3x^5-5x^3+1$
   1. Find all the critical points of $g(x)$.
   2. Find the regions where $g(x)$ is increasing and where it is decreasing.
   3. Find the regions where $g(x)$ is concave up and where it is concave down.
   4. Find all inflection points of $g(x)$.
   5. Using the first or second derivatives of $g(x)$ decide which of the critical points are local maximum values and which are local minimum values.
   6. Using only the information that you have gathered so far, sketch a graph of $g(x)$ showing this information.