exam2-practice

# exam2-practice - Name: MATH 2200, Fall 2009 Exam 2 PRACTICE...

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Name : MATH 2200, Fall 2009 Exam 2 — PRACTICE Please hand only only clearly written work, not scratch paper. Clearly mark your ﬁnal an- swers for each problem. Partial credit will only be given on problems for which your work is clearly shown. The only allowable materials for this exam are paper, pens and pencils. No notes, textbooks or calculators will be allowed.

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(1) Consider the function f ( x ) = 3 x 2 + 2 x - 1 on the interval [1 , 3] (a) Find all critical points of f ( x ) on this interval. Critical points: (b) Find the x -values at which the minimum and maximum of the function are achieved. Minimum at x = Maximim at x = Please show your work clearly below.
(2) Consider the function f ( x ) = x 2 - x on the interval [ - 1 , 2) (a) Find all critical points of f ( x ) on this interval (or write ‘none’). Critical points: (b) Construct sign chart for the derivative of f ( x ) in the space below, illustrating where the function f ( x ) is increasing and decreasing. Show your work below: (c) Find the minimum value obtained by f ( x ) on the given interval: minimum value :

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(3) Consider the function f ( x ) = 3 x 3 + x on the interval ( - 1 , 1 / 3) (a) Find all critical points of f ( x ) on this interval (or write ‘none’). Critical points: (b) Construct sign chart for the derivative of f ( x ) in the space below, illustrating where the function f ( x ) is increasing and decreasing. Show your work below: (c) Find the maximum value obtained by f ( x ) on the given interval: maximum value :
(4) A company would like to construct a cylindrical can with an open top at a ﬁxed cost of \$200

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## This note was uploaded on 12/10/2011 for the course MATH 2200 taught by Professor Kazez during the Fall '08 term at UGA.

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exam2-practice - Name: MATH 2200, Fall 2009 Exam 2 PRACTICE...

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