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7.2-Second Derivative .pdf

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MATH 157
Chiaka Drake

1 Chapter 7.2 Applications of the Second Derivative Question: You are able to determine where the graph of a function f is ____________ or ____________. However, a function can increase like this or like this , and similarly, a function can decrease like this or like this . _____ can you determine which way it is? Concavity: Let the function y f (x) be __________________ on an interval (a,b) . Then, f is concave up on (a,b) if f is __creasing on (a,b) ; f is concave down on (a,b) if f is __creasing on (a,b) . Inflection Point: is the point on the graph of f where the tangent line __________ and a ______________ in concavity occurs. Point of Diminishing Return: is the ___________ term for a point of inflection. It means you get too little out from what you put in. 2 Concavity Test: Suppose f is _________ differentiable on an open interval (a,b) . If f (x) 0 for all x in(a,b), then f is concave ____ on (a,b) . If f (x) 0 for all x in(a,b), then f is concave ____ on (a,b) . Answer: 1. Find all critical numbers of ____ and all numbers where f is ______________. Place these numbers on the real number line. This ______________ the number line into open intervals. 2. ______________ a number in __________ interval. 3. __________ the __________________ Test to these numbers to decide if f is concave ________ or concave ________ on these intervals. 3 Exa
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