Math 270 Test 4
Due Friday, July 25
Name _________________________
Circle your final answer(s) for each problem.
Since this is a takehome exam, I expect
you to show all your work and clearly explain any difficult steps.
You have a week to
finish this, so I expect to see a week’s worth of effort and polish on the finished product.
I want to see functions you write, derivatives you take, equations you solve, graphs you
use, pictures you sketch, etc.
Feel free to use your calculator, but let me know where you
do so; for example, you might write an equation with solutions and put ‘calc’ next to it.
1. Find all critical points of
4
3
( )
(2
)
f x
x
x
=

.
Classify each critical point as a maximum,
minimum, or neither.
2. For
( )
2cos(2 ) sin( )
f x
x
x
=

and 0
≤
x
≤
2
π
, find the value(s) of
x
for which
f(x)
has
a global maximum or global minimum.
3. Find the best possible bounds for each of the following functions.
(a)
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 Summer '08
 VAKARIETIS
 Math, inch margins, best possible bounds, coneshaped coffee filter

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