Second derivative test example

• [DOC File]The First and Second Derivative Tests

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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 test …

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• [DOC File]Extrema and the Mean Value Theorem

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  The Second Derivative Test cautions us that this may be the case since at at So now we wish to use all that we have learned from the First and Second Derivative Tests to sketch graphs of functions. The following table provides a summary of the tests and can be a useful guide in sketching graphs.

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• [DOC File]Section 1 - Radford University

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  Second Derivative Test (Test For Relative Maximum and Relative Minimum Points) Let f be a function where x = c is a critical point where . 1. If , then is a relative minimum. 2. If , then is a relative maximum. 3. If or is undefined, the test fails – use the 1st derivative test. Procedure For Graphing Functions Using Derivatives. Given a ...

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• [DOC File]CURVE SKETCHING EXAMPLES - Academics

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  5. Test critical points for max/min: SECOND DERIVATIVE TEST. a) take the second derivative: f ''(x) = f ''(x) = b) substitute x-coord (crit. pt.) f ''(0) = = (negative max) c) label your points: (0,1/9) : maximum. or: FIRST DERIVATIVE TEST. a) f(x) is increasing before x = 0 and. decreasing after x = 0 (0,1/9) : maximum. 6. Concave up/concave down:

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• [DOCX File]§4.1 Maximum and Minimum Values

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  The Second Derivative Test. Suppose f'' is continuous on an open interval containing c . If f ' c =0 and f '' c >0 , ... Example. Apply the second derivative test to find the . x -coordinates of the maxima and minima of . f x = x 3 -2 x 2 +x . Solution. Start by finding the critical numbers.

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• [DOC File]Optimization - Tredyffrin/Easttown School District

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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 …

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• [DOC File]New Chapter 3

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  The second derivative test implies that if 23 trees are planted per acre, the yield will be maximized with a value of . Inventory control is a very important question for many companies. For example, a furniture store expects to sell 700 sofas next year.

  second derivative test for extrema

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