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Calculus I - Test #3 Fall 2004: Maxima, Minima, Point Motion, Inscribed Rectangle, Exams of Calculus

A calculus test from math 120, fall 2004. The test covers topics such as determining maximum and minimum values of functions, point motion, finding the dimensions of the rectangle of largest area inscribed between a parabola and the x-axis, and identifying critical and inflection points. The test includes multiple-choice questions and requires the application of calculus concepts.

Typology: Exams

Pre 2010

Uploaded on 08/07/2009

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Calculus I Math 120 Fall 2004
Test #3 Name: (print neatly)
Instructor: (sign)
1. (30 pts) Consider the function f(x) = x55x3+ 10x
6.
a) Determine the maximum and minumum values of f(x) on the closed interval [1,4]?
b) Determine the maximum and minimum values of f(x) on the open interval (0,4)?
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Calculus I – Math 120 Fall 2004

Test #3Instructor: Name: (print neatly)(sign)

  1. (30 pts) Consider the function f (x) = x^5 −^5 x 63 + 10x. a) Determine the maximum and minumum values of f (x) on the closed interval [1, 4]?

b) Determine the maximum and minimum values of f (x) on the open interval (0, 4)?

  1. (10 pts) Suppose a point is moving along the curve y = x^2 , and that at t = 1 the point is at (2, 4) and moving such that dxdt = −2 units/sec. At t = 1, is the length of the straight segment from the point on the curve to (0, 7) increasing or decreasing?
  1. (20 pts) Let f (x) = x^4 − 8 x^3 + 18x^2. a) Find all critical values oflocal maximum, local minimu, or neither. f (x) and apply either the first or second derivative test to classify each as a

b) Find all inflection values of f (x).

c) Which of the following graphs most closely shows the behavior ofi) ii) iii) iv) f (x)

i)^0 -^1 0 1 2 3 4 5

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ii)^0 -^1 0 1 2 3 4 5

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iii)^0 -^1 0 1 2 3 4 5

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iv)^0 -^1 0 1 2 3 4 5

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  1. (20 pts) The graph of f (x) is given at the bottom of the page. a) Place a filled dot, a, b, c,.. ., from left to right. • , over each critical point on the graph and label them with lower case letters,

b) Place an open dot, A, B, C,.. ., from left to right. ◦, over each inflection point on the graph and label them with upper case letters,

c) List all labelled points which are local maxima,. d) Give the label of a local maximum at which the second derivative test can not be applied,. e) Give the label of a critical point at which the second derivative test would be inconclusive,. f) Give two labelled points such that the arc between them is concave up and decreasing,.