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Unformatted text preview: x 2 2 3 and the derivative of h is given for all x L 0 . x (a) Find all values of x for which the graph of h has a horizontal tangent, and determine
whether h has a local maximum, a local minimum, or neither at each of these values.
Justify your answers.
(b) On what intervals, if any, is the graph of h concave up? Justify your answer.
(c) Write an equation for the line tangent to the graph of h at x = 4.
(d) Does the line tangent to the graph of h at x = 4 lie above or below the graph of h for
x 4 ? Why? £ 1:x o 2
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discontinuity at 0
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¥ (a) h a(x ) 0 at x o 2
h =(x ) x + und 0
2 0 Local minima at x 0+
2 2 and at x 2 2
0 for all x L 0 . Therefore,
x2
the graph of h is concave up for all x L 0 . (b) h aa(x ) 1 (c) h a(4) y 16 3 2
4 7
(x
2 £ 1 : h aa(x )
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3 : ¤ 1 : h aa(x ) 0
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¦ 1 : answer
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¥ 7
2 4) 1 : tangent line equation (d) The tangent line is below the graph because 1 : answer with reason the graph of h is concave up for x 4 . Copyright © 2001 by College Entra...
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This document was uploaded on 05/03/2012.
 Spring '09
 Calculus

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