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Unformatted text preview: the graph has 4 critical points and 2 local maxima, property (iii) fails in keywords: Stewart5e, critical point, local maximum, inflection point 4 2 4 2 2 4 Use calculus to decide which of the following is the graph of f (x) = 3x2/3 + 2x . 008 (part 1 of 1) 10 points because the graph is concave DOWN on (4, 2), property (iv) fails in 4 2 4 2 2 4 1. because the graph is concave UP on (0, 2), and property (v) fails in Garcia, Ilse Homework 11 Due: Nov 6 2007, 3:00 am Inst: Fonken After differentiation of 2. we see that f (x) = in particular, (i) f has critical points at x = 1, 0. 3. corDifferentiating again we next see that f (x) =  2 , 3x4/3 2 x1/3 +2 = 2(x1/3 + 1) ; x1/3 f (x) = 3x2/3 + 2x 9 from which it follows that (ii) f < 0, so f concave down, on (, 0), rect and again (iii) f < 0, so f concave down, on (0, ) ; 4. in particular, f has a local maximum at x = 1. Of the five graphs only 5. has these properties. keywords: Stewart5e, fractional point, critical point, loca...
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This note was uploaded on 01/16/2009 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas at Austin.
 Spring '08
 schultz
 Differential Calculus

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