First derivative second derivative graph

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

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  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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• MATH 201

  8. Use first and second derivatives to sketch curves and to solve optimization problems. 9. Relate antiderivatives and integrals. 10. Calculate definite and indefinite integrals by substitution. 11. Use derivatives and integrals to solve practical problems. Use a scientific and/or graphing calculator proficiently as related to coursework.

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• [DOC File]Assignments Differentiation

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  second derivative of a function g. From the graph, determine. a. On what interval(s) is the graph of g concave up? concave down? b. Where does the graph of g have points . of inflection? 4. In the diagrams a – d below represent the graphs of four different functions while (1) – (4) represent the second derivatives of those functions. Match ...

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• [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 …

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• [DOC File]New Chapter 3

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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 the way they are increasing.

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• [DOC File]AP Calculus Assignments: Derivative Techniques

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  Find the equation of the line tangent to the graph of at x = 9. 7. a. Sketch a graph of a continuous function f having f ' > 0 for all x. b. Does the function you sketched in part (a) have an inverse function? HDYK? c. Hypothesize a general rule about the derivative of a continuous function f …

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• [DOC File]Section 1 - Radford University

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  First Derivative Test. Section 3.4 Concavity and The Second Derivative Test. Practice HW from Larson Textbook (not to hand in) p. 177 # 1-29 odd, 33, 39, 47, 49. p. 185 # 1-29 odd . Increasing and Decreasing Test for Functions. Given a function f defined on an interval. 1.

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• [DOC File]Derivatives - UH

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  In both of these cases, the graph is increasing. If the derivative is −0.3, that’s a small negative change. If it’s −57, that’s a good sized negative change. In both of these cases, the graph is decreasing. Popper 09, Question 2 Shortcuts to getting the derivative: First let’s do …

  graph of second derivative

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• [DOC File]New Chapter 3

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  6.2 The Second Derivative. Since the derivate of a function is a function itself it is possible to take its derivative. The derivative of the first derivative is called the second derivative and it is typically denote using a double prime, . The second derivative of a function is a function itself and therefore has its own derivative.

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• RELATING A FUNCTION TO ITS DERIVATIVE

  on the first derivative graph. Acknowledge that points of inflection are the x values of the maximum and minimums on the first . derivative graph and the zeros on the second derivative graph as well as the change in concavity . of the given function. PRIOR KNOWLEDGE. Students need to be able to graph …

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