Functions : Concave Up and Concave Down

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  (a) Yes (b) In this case (when both f and g are degree 2 functions), f(x) + g(x) will be concave up for some functions and concave down for some other functions, depending upon the magnitude of the leading coefficients of f(x) and g(x). (c) No.

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  The expert determines the intervals on which functions are concave up and concave down.

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  56924 Find the interval in which the given functions 10xe^(-x) and x^2-4/x+1 are concave up or down For each of the following equations, would you please state the intervals for which it is concave up and for which it is concave down?

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  Since x=-2 is a minimum, then the function concave up at this point, and the function concaves down at x=4. So the interval is for the function to concave up. Here is the curve for the function for you to better understand it.

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  Thus all extreme points of are at and at . 3) Since , then when , and thus is concave up; when , and thus is concave down. 4) Set , . So the inflection point of is . 5) The graph of is shown below.

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  f(x) is concave up when f"(x) > 0 f(x) is concave up when f"(x) > 0 f(x) is concave down when f"(x) < 0 Point of inflection occurs when f"(x) = 0 for each of the above functions complete the following table.

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  From the second derivative test , we can conclude that The graph is concave down in the interval (-infinity, -2] and (0, 2) Concave down in the interval (-2,0) and [2.