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You are not logged in. #1 20130101 11:51:25
Second DerivativeJust drafted this: Second Derivative "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #2 20130101 12:01:54
Re: Second DerivativeHi MIF; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20130101 21:50:26
Re: Second DerivativeHappy New Year MathsIsFun, You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #4 20130101 21:57:14
Re: Second Derivative
I do NOW ... "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #5 20130102 00:08:08
Re: Second DerivativeHi MathsIsFun, Character is who you are when no one is looking. #6 20130102 06:56:52
Re: Second DerivativeIt would be nice to have a link to a calculator that can calculate these derivatives for the common functions and graph f, f' and f'' in different colors on the same set of axes. Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #7 20130102 07:09:00
Re: Second DerivativeYou mean this? #8 20130102 07:22:17
Re: Second DerivativeThat's nice and a good site to remember. It only lacks a graph of f, f' and f'' on the same set of Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #9 20130102 07:27:31
Re: Second DerivativeHi noelevans; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #10 20130102 07:51:33
Re: Second DerivativeThanks bobbym, Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #11 20130102 08:13:31
Re: Second DerivativeHi noelevans; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #12 20130102 09:35:59
Re: Second Derivative
As in "y=3.105x+2.09" ? "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #13 20130102 09:43:37
Re: Second DerivativeHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #14 20130102 09:46:11
Re: Second Derivative
Sure will. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #15 20130114 22:20:25
Re: Second Derivativehi MathsIsFun Find the turning points, and identify if each is a maximum, minimum or point of inflection. The turning points of a function are places on the curve where the gradient is momentarily zero. First differentiate the function. Solving this quadratic gives Substituting these into the original function means the turning points are at (1/3 , 0.18519) and at (1 , 1) The first graphs below show the function in blue and the derivative function in red. Notice that the two places where the red curve crosses the x axis line up with the turning points of the function. Now, if you have the graph in front of you, it is obvious that the first is a maximum and the second a minimum. But what if you have to prove it without referring to the graph ? Differentiate the gradient function. So the gradient of the red curve at x = 1 is negative. Without having to see the graph I know the red curve crosses the x axis from positive values to negative values as x increases from less than 1 to more than 1. So I know the blue curve goes from a positive gradient, through zero, to a negative gradient. So it must be a maximum. So the gradient of the red curve at x = 1/3 is positive. Without having to see the graph I know the red curve crosses the x axis from negative values to positive values as x increases from less than 1/3 to more than 1/3. So I know the blue curve goes from a negative gradient, through zero, to a positive gradient. So it must be a minimum. The red curve is repeated along with its gradient function (the double differentiated function) in blue on the second graphs below. I have put little + and  signs close to the turning point values to show how the red curve goes from + to  or from  to + Rule for identifying maximums and minimums: Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #16 20130115 07:32:13
Re: Second DerivativeGreat example, will adapt it to web page. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #17 20130115 07:40:26
Re: Second DerivativeThank you. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #18 20130116 10:58:47
Re: Second Derivativehi MathsIsFun
Try to answer these questions:
Try to answer these questions:
finish as before You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #19 20130117 09:38:46
Re: Second DerivativeHi Bob, "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #20 20130118 13:13:08
Re: Second DerivativeGreat,but make it a it longer.great calc. Hey. 