Second derivative of a function

• [DOC File]Calculus Review

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  Use the First and Second Derivative Tests to find absolute maximum and minimum values of a function. Use the First and Second Derivative Tests to solve optimization applications. Introduction. In this lesson we wish to extend our discussion of extrema and look at the absolute maximum and minimum values of functions.

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• [DOC File]The First and Second Derivative Tests

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  The original function takes x and computes the second coordinate for the graph point at x. The derivative takes x and computes the instantaneous rate of change of the function at x. Let’s look at a table of these: x Graph point. Slope of tngt l (2 (8 12 (1 (1

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• [DOCX File]www.uhigh.ilstu.edu

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  Set the second derivative equal to 0 and solve for x. Substitute the x-value in the equation of the original function to find the corresponding y-value. (A point of inflection may also occur at values of x for which . is undefined, but we will not consider these cases.) APPLICATIONS OF POINTS OF INFLECTION: 1.

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• [DOC File]CALCULUS

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  the sign of the derivative is connected to the function being increasing or decreasing. Draw a diagram to help you explain. Go to the second page of the Sketchpad document.

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• [DOC File]Derivatives - UH

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  Second Derivative Test: (another way to determine relative extrema) Let f′ and f′′ exist at every point in an open interval (a,b) containing c and suppose f’(c) = 0. 1. If f′′(c) < 0 (function is concave down at x=c), then f(c) is a relative maximum.

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• [DOC File]MAC 2233

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  The second derivative can be used to study the shape of the graph of a function. For example both and are increasing in the interval (0, ∞), but there is a fundamental difference in …

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• [DOC File]Section 1

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  The second derivative test indicates whether the point is a . maximum. or . minimum. If the first derivative,at x = x0, then the value of the function at the point x0 will be a (i) relative maximum if the second derivative is , (ii) relative minimum if the second derivative is . An inflection point

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• [DOC File]GRAPHING OF FUNCTIONS USING FIRST AND SECOND …

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  9. The graph of the second derivative, , of a function f is shown. State the x-coordinates. of the inflection points of f. Justify your answer. TURN->>> 10. The function h is defined by , where f and g are the functions whose. graphs are shown below. (a) Evaluate . (b) Estimate .

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• [DOC File]New Chapter 3

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  If the second derivative test fails, then the first derivative test must be used to classify the point in question. Ex. f (x) = x2 has a local minimum at x = 0. Ex. f (x) = x4 has a local minimum at x = 0. But the second derivative test would fail for this function, because f ″(0) = 0. The first derivative …

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• Second Derivative Calculator with Steps - Online & Free!

  3. If the second derivative f'' is positive (+) , then the function f is concave up . 4. If the second derivative f'' is negative (-) , then the function f is concave down . 5. The point x=a determines a relative maximum for function f if f is continuous at x=a , and the first derivative f' is positive (+) for xa .

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