First derivative test examples

    • [DOC File]CURVE SKETCHING EXAMPLES - Academics

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      = 0 (zero test fails, must use the first. derivative test) f ''(1) = 60(1)3 - 30(1) = 30 (positive min) c) label your points: (-1,2) : max (1,-2) : min (0,0) : unknown at this time. or: FIRST DERIVATIVE TEST. a) f(x) is increasing before x = -1 and . decreasing after x = -1 (-1,2) is a maximum. b) f(x) is decreasing before x …

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    • [DOC File]Optimization Problems (Calculus Fun)

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      The restrictions stated or implied for such functions will determine the domain from which you must work. The function, together with its domain, will suggest which technique is appropriate to use in determining a maximum or minimum value - the Extreme Value Theorem, the First Derivative Test, or the Second Derivative Test. 1.

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    • [DOC File]Math 131

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      - Rates of change: derivative at a point. Math 145 - Calc I. Review for Test 2. Test 1 will consist in 5 problems. You are allowed a ½ page with formulas on one side only, but with no examples or solutions. The page should be turned in, together with the exam. Review the theory first…

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    • [DOC File]Fundamentals of Engineering Exam Sample Questions

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      Consider a function of x equal to the determinant shown here: . The first derivative of this function with respect to x is equal to. Questions 16-18, relate to the three vectors . A, B, and . C. in Cartesian coordinates; the unit vectors . i, j, and . k. are parallel to the x, y, and z axes, respectively. A = 2. i +3. j + k B = 4. i-2. j-2. k C ...

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    • [DOCX File]VOCABULARY: derivative, first derivative, second ...

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      Apr 13, 2001 · VOCABULARY: derivative, first derivative, second derivative, product rule, quotient rule, chain rule, implicit differentiation, logarithmic differentiation, differentials, related rates, optimization, maxima and minima, First Derivative Test, 2nd Derivative Test, L'Hospital's Rule, Indeterminate Forms, Newton's Method, Antiderivatives ...

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    • [DOC File]Section 1

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      Understand and use the First Derivative Test to determine min’s and max’s. Understand and use the Second Derivative Test to determine min’s and max’s. Vocabulary: Increasing – going up or to the right. Decreasing – going down or to the left. Inflection point – a point on the curve where the concavity changes. Key Concept:

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

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      To see more examples of worked out problems involving finding minima and maxima on an interval (11.0), see the video at Khan Academy Minimum and Maximum Values on an Interval (11:41). This video shows the process of applying the first derivative test to problems with no context, just a …

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    • [DOC File]Extrema and the Mean Value Theorem

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      We applied the First Derivative Test to find extrema and sketch graphs. Multimedia Links. For more examples on determining whether a function is increasing or decreasing (9.0), see Math Video Tutorials by James Sousa, Determining where a function is increasing and decreasing using the first derivative …

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    • [DOC File]Primer on Differentiation: General Engineering

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      The knowledge of first derivative and second derivative of a function is used to find the minimum and maximum of a function. ... 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. ... Below are some examples to show real-life ...

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