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[DOC File]GRAPHING OF FUNCTIONS USING FIRST AND SECOND …
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(1st Derivative Test for Monotonic Functions)Suppose that is continuous on and differentiable on .If at every point , then is strictly increasing or increasing on .If at every point , then is strictly decreasing or decreasing on . Is the converse of this statement true, that if . f is .
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[DOCX File]www.lonestar.edu
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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.
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[DOCX File]M. Olsen's Website
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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 ...
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[DOC File]Chapter 2, sections 2
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- 1st Derivative Test for Monotonic Functions - 1st Derivative Test for Local Extrema 4.4 Concavity and Curve Sketching - Concavity: definition, 2nd derivative test - Points of inflection - 2nd Derivative Test for Local Extrema - Strategy for Graphing y=f(x) - Learning about functions from derivatives.
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[DOC File]Section 1 - Radford University
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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]1st derivative Test WS
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1st and 2nd Derivatives. The first derivative . f’ of . f. tells us where . f. is increasing and where . f. is decreasing, while the second derivative . f” of . f. tells us where . f. is concave upward and where . f. is concave downward. Finding Relative Extrema (1st Derivative Test) Determine the critical points of . f. Find the 1st ...
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[DOC File]The First and Second Derivative Tests
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1st derivative Test WS Name _____ Where is function f increasing? decreasing? Constant? When is…. Look at the following sketch and . answer the following questions. The graph of is given above. The domain of f is . (a) For what value(s) of x, , is the graph of f increasing? Justify your answer.
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Calculus - Derivative Test (worked solutions, examples, videos)
The first derivative test gives the correct result. Ex. Use the second derivative test to find the local extreme points of . h(x) = 2x3 − 18x. Comment: It’s important to remember that in the first derivative test we check the intervals between critical points, by evaluate f ′ at some test point in each interval.
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1st derivative test