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ECO 310, Fall 2008
Problem Set 1: Review of Optimization
Due in class on September 30
Question 1
Note: Your graph in part (a) should suggest how to proceed in parts (b)(e), but
you must check the appropriate calculus conditions for your answers to those
parts.
Consider the realvalued function
f
deﬁned over the interval [

10
,
10] by
f
(
x
) =
(
x
(
x

4)
if

10
≤
x
≤
0
,
10
x
(8

x
) if 0
< x
≤
10
.
(a) Sketch a rough graph of the function. Use a calculator or a computer
program such as Mathematica if you can; else calculate a few values by
hand. Integer values of
x
will suﬃce to give you a good idea.
(b) Find all critical points of the function. Identify the local maxima and
minima.
(c) Is the function discontinuous anywhere? Is the function nondiﬀerentiable
anywhere? Is there a local maximum or minimum at this point?
(d) Does the function have any local maxima or minima at its endpoints?
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This note was uploaded on 10/13/2008 for the course ECO 310 taught by Professor Stephene.morris during the Fall '08 term at Princeton.
 Fall '08
 StephenE.Morris

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