B on what intervals if any is the graph of h concave

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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 ¦ ¦ ¦ ¦ 1 : analysis ¦ ¦ 4:¦ ¤ 2 : conclusions ¦ ¦ ¦  1 > not dealing with ¦ ¦ discontinuity at 0 ¦ ¦ ¥ (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 ) ¦ ¦ ¦ ¦ 3 : ¤ 1 : h aa(x )  0 ¦ ¦ ¦ 1 : answer ¦ ¦ ¥ 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.

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