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UFCalcSet27 - Exercises UF Calculus Set 27 1 For the...

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Exercises UF Calculus Set 27 1. For the polynomials below, calculate the intervals of increase/decrease and concavity. Use these, the intercepts, and end behavior to sketch their graphs. (a) f ( x ) = x 4 + 2 x 3 (b) f ( x ) = x (3 - x ) 4 (c) f ( x ) = (1 - x 2 ) 5 Count the number of turning points and inflection points, and consider how this relates to the multiplicity of the roots to f 0 and f 00 for polynomials. 2. Graph the functions below. In the process, consider each of the following details to use in your graph. (1) Domain; x, y -intercepts, when calculable (2) interval(s) on which the function increases/decreases (3) interval(s) on which the function is concave up/down (4) critical numbers, local extrema, inflection points (5) asymptotes, local behavior at discontinuities/endpoints of domain (a) f ( x ) = 2 x 3 + 6 x (b) f ( x ) = 20 x 4 x 2 + 1 (c) f ( x ) = x + 1 x 2 (d) f ( x ) = ln x x 2 (e) f ( x ) = x 15 - x (f) f ( x ) = x 2 15 - x (g) f ( x ) = x 1 / 3 (6 - x ) (h) f ( x ) = 4 x 2 / 3 4 + x (i) f ( x ) = x 2 + 8 ln( x ) - 10 x (j) f ( x ) = x ln( x ) (k) f ( x ) = xe 1 - x 2 (l) f ( x ) = e x 1 - x (m) f ( x ) = e - 1 /x (n) f ( x ) = 2 e - x + e x/ 4 3. Graph the functions below. In the process, consider the details as in Exercise 2 to use in your
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