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[DOC File]Math 202 – Test 2 Review
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Apr 13, 2001 · LESSON TOPIC:The Derivative in Graphing and Analysis of Functions. BIG IDEAS: (Content standards, assessment anchors, eligible content) objectives, and skill focus) ... maxima and minima, First Derivative Test, 2nd Derivative Test, L'Hospital's Rule, Indeterminate Forms, Newton's Method, Antiderivatives. STUDENT OBJECTIVES (COMPETENCIES ...
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[DOC File]MATH 22 COMMON FINAL EXAM - High Point University
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(2nd derivative test). Solve max/min and related rates problems using calculus. Obtain approximations using differentials and Newton's Method. Anti-differentiate algebraic and trigonometric functions, including the technique of u-substitution. Be able to evaluate constants of integration for the indefinite integral.
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[DOC File]2006 AP Calculus AB – Part A (with calculator) - Solutions
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When the cubic has a MAXIMUM the 2nd derivative is a NEGATIVE number. When the cubic has a MINIMUM the 2nd derivative is a POSITIVE number. When the cubic has an INFLECTION point the 2nd derivative is ZERO. Unfortunately, the test does not always work! Sometimes if d2y = 0 it can be a MAX or a MIN instead of a point of inflection. dx2 . y = x4
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[DOC File]Section 1 - Radford
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Be able to evaluate the 2nd derivative of a function in a given interval to determine whether the function is concave up or concave down in that interval. Be able to identify maximum or minimum points of a function through consideration of points where the first derivative is 0, followed by consideration of the 2nd derivative at any such point.
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[DOCX File]MATH 201 – CALCULUS I
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The 2nd derivative will be the coefficient of the . linear term as with: and (ii) 2nd Derivative Test. From above and (concave up) Then . and 1pt – integrand. where 1pt – for . and we obtain: 1pt – answer (b) hence: = 34.198 or 34.199 (Here 2 pts for the integrand and 1 pt only for limits of integration, constant, and answer) ...
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[DOCX File]VOCABULARY: derivative, first derivative, second ...
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the 1st derivative test for relative extrema, the 2nd derivative test for relative extrema, finding intervals on which a function is decreasing, increasing, concave up, concave down, finding inflection points, criteria from in-class handout (and text, too) for finding equations of vertical and horizontal asymptotes for the graph of a function ...
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[DOC File]MAT 117 .edu
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This is the familiar (except for the leading 4) expression for the second derivative test in multi-variable functions. The “4” is a result of the fact we only studied one type of surface (the second-degree two-variable case). Conclusion.
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[DOC File]An Informal Proof/Demonstration of the Second Derivative Test
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To test these points, we first try the 2nd derivative test using . This gives the following information for each candidate. This says the graph is concave down at this point or that (8, 4) is a local maximum. Hence, the 2nd derivative test says (8, 4) is a local maximum but is inconclusive for the point (0, 0). So we need more information.
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[DOC File]The First and Second Derivative Tests
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MAT 210 Practice – 2nd Derivative Test for Extrema (plus). 1) If the first derivative of a function equals zero when x = c, what do we know? a) A local maximum exists when x = c. b) A local minimum exists when x = c. c) Either a or b. d) A horizontal tangent line exists at x = c.
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Second partial derivative test - Wikipedia
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 gives the correct result.
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2nd derivative test