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.

Javier Fernandez 2004-03-23