Using the second derivative test
[DOC File]CALCULUS
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WORKSHEET ON DERIVATIVES. Work the following on notebook paper except for problems 11 – 12. Do not use your calculator. On problems 1 – 4, find the critical points of each function, and determine whether they are relative maximums or relative minimums by using the Second Derivative Test …
[DOC File]An Algorithm for Curve Sketching - THANGARAJ MATH
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Then use second derivative test with number smaller and bigger than 0 Find inflection points by subbing d2y/dx2 = 0 f(x) = x3 + 2x2. f’(x) = 3x2 + 4x. f’’(x) = 6x + 4. 0 = 6x + 4-4 = 6x x = -2/3 is an inflection point Determine any oblique asymptotes. Identify if the functions …
[DOC File]CALCULUS
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WORKSHEET ON DERIVATIVES 2nd derivative test. Work the following on notebook paper except for problems 11 – 12. Do not use your calculator. On problems 1 – 4, find the critical points of each function, and determine whether they are relative maximums or relative minimums by using the Second Derivative Test whenever possible. 1. 3. 2. 4.
[DOC File]The Apple Orchard Problem
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Quadratic Regression, First Derivative Test, Second Derivative Test, Critical Points. Background Knowledge: This activity will have the students exploring the maximum number of trees to add to an orchard before production starts to decline. Students should have a general understanding of how to find the minimum and maximum of functions using a ...
[DOC File]Topic 7: Calculus
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Justification using second derivative test:-.006 < 0 Therefore, when x = 20,000, the curve is concave down and the value is a maximum. 7.4. Definition of Antiderivative: A function is an Antiderivative of F on an interval I if for all x on I. Indefinite integral interpreted as a family of curves. Indefinite integrals of: With Linear function ax ...
[DOC File]First and Second Derivative Tests Quiz
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Using analytic methods, find the intervals over which the function is increasing, decreasing, concave up and concave down. Find all extrema and state them properly. Find all the points of inflection and state them as ordered pairs. Finally sketch the function. ... First and Second Derivative Tests Quiz ...
[DOC File]GRAPHING OF FUNCTIONS USING FIRST AND SECOND …
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THE SECOND DERIVATIVE TEST FOR EXTREMA (This can be used in place of statements 5. and 6.) : Assume that y=f(x) is a twice-differentiable function with f'(c)=0 . a.) If f''(c)0 then f has a relative minimum value at x=c . These are the directions for problems 1 through 10.
[DOC File]New Chapter 3
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Using the Second Derivative Test, the function has an absolute maximum at x = 5, and the absolute maximum value is. See the following figure. (Figure 7.5 Graph of (Applications . We now turn our attention to illustrate how calculus can be used to solve real-world optimization problems.
[DOC File]Section 1 - Radford
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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 ...
[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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