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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.
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Test #3Instructor: Name: (print neatly)(sign)
b) Determine the maximum and minimum values of f (x) on the open interval (0, 4)?
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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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,.
