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Unformatted text preview: Lecture 20 1 Lecture 20: (Sec. 4.2, Part I) Applications of the Second Derivative: Con cavity ex. Total sales S (in hundreds of dollars) of a prod uct are related to the amount of money x spent on ad vertising according to the function S ( x ) = . 002 x 3 + . 6 x 2 + x + 500 where x is measured in hundreds of dollars and 0 x 200. Consider the graph of S ( x ) and its tangent lines: Lecture 20 2 Def. Let function f be differentiable on an open interval ( a, b ). The graph of f is 1) concave upward (concave up) on ( a, b ) if 2) concave downward (concave down) on ( a, b ) if NOTE: f is concave upward (downward) at a point x = c if Lecture 20 3 Also note the following: 1) f is concave upward if 2) f is concave downward if Lecture 20 4 ex. Let f ( x ) = x 3 1) Sketch the graph of f ( x ). 2) Sketch the graph of f ( x ). Lecture 20 5 Theorem Let f be a function whose second derivative exists on interval ( a, b )....
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This note was uploaded on 07/18/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.
 Spring '08
 Smith
 Calculus, Derivative

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