please see the attached file, and show all required steps.
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+
. ( ) = −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.
3.
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
undefined.
:
( ):
−2
−1.5
−1
0
0.5
1
1.5
′( ):
′′ ( ):
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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