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First let us find the critical points. Since f(x) is a polynomial function, then f(x) is continuous and differentiable everywhere. ... So the critical points are the roots of the equation f'(x) = 0, that is 5x4 - 5 = 0, or equivalently x4 - 1 =0. Since x4 - 1 = (x-1)(x+1)(x2+1), ... These points are called critical points.
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www.sosmath.com/calculus/diff/der13/der13.html
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In Reply to: Find critical points? posted by Andrew on November 07, 2002 at 12:57:16: ... : 1) Find all critical points of y = f(x). Identify each one by its x coordinate. : 2) Use the first derivative test to determine each critical point of f(x) whether it is a local minimum, local maximum, or neither.
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library.thinkquest.org/20991/gather/calc/messages/5116....
library.thinkquest.org/20991/gather/calc/messages/5116.html
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Finding them is easy. Calculate the derivative, equate it to zero and solve the resulting equation. ... The curves y = x3, y = x4, y = 1 - x4 all have critical points at x = 0 and all have y'' = 0. The first is a point of inflexion, the second a local minimum and the third a local maximum. You check these for yourselves.
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www.maths.abdn.ac.uk/~igc/tch/eg1006/notes/node59.html
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Find all critical points of f and find extreme values (maxima and minima) and saddle points of f. Please see the attached file ... Critical points, extrema and saddle points are found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
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www.brainmass.com/homework-help/math/calculus/54356
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For the following function, find the critical points, determine their nature (maxima, minima, inflection, etc.) and clearly sketch the function showing all the coordinates: h(x, y) = (x^2 - 4)^2 + y^2 ;
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www.brainmass.com/homework-help/math/calculus/93777
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Fisher Distribution Critical Point Calculator ... How to use this applet: ... Click on the Update Button to draw graph and display critical point...
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www.acs.ucalgary.ca/~nosal/src/Applets/F-Crit/Fcrit.htm...
www.acs.ucalgary.ca/~nosal/src/Applets/F-Crit/Fcrit.html
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CiteSeerX - Document Details (Isaac Councill, Lee Giles): Most minimax theorems in critical point theory require one to solve a two-level global optimization problem and therefore are not for algorithm implementation. ... 4 Remarks on Finding Critical – Brezis, ... 3 Instability indices of saddle points by a local minimax method,
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citeseer.ist.psu.edu/447829.html
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CiteSeerX - Document Details (Isaac Councill, Lee Giles): Introduction Let H be a Hilbert space and J ). Denote #J its Frechet derivative and J # its gradient. ... The objective of this research is to develop computational theory and methods for finding multiple critical points, i.e., solutions to the Euler...
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citeseer.ist.psu.edu/zhou02computational.html
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into Mathematica. Equations defining the critical points are given by ... To see what the second derivative test says for the critical points found above, we can just use the fact that the solutions come out as substitutions to jam the critical points into the test.
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www.math.tarleton.edu/Faculty/White/calclab/node7.html
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