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Math 210: Written Homework 3, due April 3rd
Instructions: All answers must be simplified! Show all your work. You may not use a
graphing calculator to justify any steps but you may want to use a graphing utility to check your
final graph.
Use the graphing guidelines from the book (below) to graph the following functions:
( ) =

. ( ) = −2 5 + 5 3
Make sure to clearly mark on your graphs all the relevant points (intercepts, local min/max,
inflection points). You need to show sufficient work as to provide complete answers to ALL
9 guideline items. Circle your answers where appropriate and proceed in the order indicated
by the guidelines.
Regarding item #3: for these two functions, you DO need to compute both the first AND
second derivatives, but you may choose which test you use to determine local max/min.
a. In the table, state whether ( ), ′( ) , and ′′( ) are positive(+),
negative(-), or zero(0) at the given values of . You do not need to state your reasoning.
Note that, for this particular function, there are no values for which , ′ , ′′ are
( ):
′( ):
′′ ( ):
b. Which of the above x-values are critical points?
c. Which are relative extrema (this will be close to, but not exactly the same as your
answer to part b), and what are the relative extrema?

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