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[DOCX File]VOCABULARY: derivative, first derivative, second ...
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Recall that tells us where f is increasing and where it is decreasing. The derivative of , which is , tells us where is increasing and where it is decreasing. We can use the following second derivative test for concavity. (Table 5.9 Test for Concavity . If on the interval (a, …
first and second derivative rule

[DOC File]Chapter 10 Multi-Variable Functions
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Apr 13, 2001 · There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. ... derivative, first derivative, second derivative, product rule, quotient rule, chain rule, implicit ...
second derivative test examples

[DOCX File]VOCABULARY: derivative, first derivative, second ...
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use rules of differentiation to differentiate functions, ... where the second derivative of a function becomes zero is a way to know whether the critical point found in the first derivative test is a local minimum or maximum. Let be a function in the interval and . ... As per the second derivative test, corresponds to a minimum. ...
first and second derivative test

[DOC File]Primer on Differentiation: General Engineering
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• Be able to find the local maximums and minimums for a function using the First Derivative Test or the Second Derivative Test. • Be able to find the inflection points of a function using the second derivative. • Be able to sketch the graph a function using information about its first and second derivatives.
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[DOC File]New Chapter 3
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Now applying the second derivative test by evaluating we get the following Since D > 0 and the second derivative test states that a relative maximum exists at the critical point. Thus, to maximize profit, the shoe company should sell a pair of aerobic shoes for $50.56 and a pair of running shoes for $70.39.
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[DOC File]AP Calculus AB
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First derivative test for extrema. Concavity and points of inflection. Second derivative test for extrema. 4.4 Modeling and Optimization (volume of a can activity) 4.5 Linearization. 4.6 Related Rates (lollipop activity) Review/Unit Exam. Unit 5: The Definite Integral (16 teaching periods) 5.1 Estimating with Finite Sums. 5.2 Definite Integrals
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[DOC File]The First and Second Derivative Tests
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3.2 –Extrema and the 1st Derivative Test. know what extrema are (both relative and absolute) be able to find them using the first derivative test. 3.3 –Concavity and the 2nd Derivative Test. understand what the second derivative tells us about the original function . know what “concavity” is and what “inflection points” are & how to ...
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[DOC File]Chapter 2, sections 2
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Feb 12, 2011 · VOCABULARY: derivative, first derivative, second derivative, product rule, quotient rule, chain rule STUDENT OBJECTIVES ( COMPETENCIES /OUTCOMES ): Extend algebraic properties and processes to quadratic, exponential, and polynomial expressions and equations and to matrices, and apply them to solve real world problems.
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[DOC File]MTH 251 - CALCULUS
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4. F, F’, F” Around the World Game- Each desk has a set of cards relating to the First Derivative Test, Test for Concavity, and the Second Derivative Test. Students are given the beginning of a phrase and must complete it with the correct card.
first and second derivative rule

The Second Derivative Rule
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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Second derivative test rules