Math 1210-001
Homework 6
Due 1 July, 2013
This homework assignment is designed to go along with sections 3.3 through
3.5 of your textbook, which we have completed in class. Make sure your work
is neat, legible, well-organized and self-explanatory. You must staple your
assignment to receive full credit.
Name:
1. (10 points) Let g(x) = (x − 2)5 .
(a) Find g 0 (x) and find all critical points of g(x).
(b) Use the Second Derivative Test to classify as many critical points of g(x) as possible.
(c) Use the First Derivative Test to classify all critical points of g(x) (even the ones
you classified in the previous part).
2. (10 points) Sketch the graph of a function f (x) which is continuous on [0, 1] with the
following properties
• f has two local maxima and three local minima in (0, 1).
• f has at least two singular points
• f has at least two stationary points
• The (global) extreme values of f are achieved on [0, 1] but not on (0, 1).
3. (10 points) Your boss wants you to design a box with a square base (not necessarily a
cube). For budgeting reasons, she would like the box to use exactly 10 square meters of
plexiglass, but does not care what shape pieces you start with. What is the maximum
volume that such a box can have?
4. (10 points) Use information from the first and second derivative, as well as information
about x and y intercepts, end behavior, etc (from MATH-1050) to graph the function
g(x) = x2 + x − 6x − 1. Label any local extrema, singular points, and points of inflection.
5. (10 points) Show that the generic quadratic function f (x) = ax2 +bx+c, where a, b, and
c are real numbers, has no inflection points by using information about its derivatives.