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Graphical link between function and derivate

  1. Nov 13, 2004 #1

    mad

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    Hello all,
    first, excuse my english I dont speak it very well

    I have a problem. We have two sheets. One are graphics of functions, and the other are graphics of the derivate of those function. Now my problem is I dont know how link a graphic of a function to the graphic of its derivate. I know that, for example, y = x^2, for ]-oo, 0[ , that the slope (sp?) will be negative. So why , on the graphic of the derivate which is y=2x, is the slope positive? How can I associate a function to its derivate?
    thanks a lot
     
  2. jcsd
  3. Nov 13, 2004 #2

    mad

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  4. Nov 13, 2004 #3
    The gradient function of y = x^2, that is: y = 2x, is negative for values of x less than zero. So, although the slope of the gradient function is positive, you can see that value of the gradient function at say, x = -2 still gives the slope of y = x^2 at x = -2.

    The slope of the gradient function would only be negative if the original function was y = -x^2.

    It helps to plot the two graphs y = x^2 and y = 2x above and below each other, and matching respective x values on both, to get a feel for what's happening in the gradient function.
     
  5. Nov 13, 2004 #4

    kreil

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    Gold Member

    The relationship is:

    When the function is increasing, the derivative is positive

    When the function is decreasing, the derivative is negative

    When the function is changing direction, the derivative is zero

    So, in the case of [tex] f(x)=x^2 [/tex] from [tex]-\infty\rightarrow 0 [/tex] the function is decreasing and the derivative is negative. At the point (0,0) the function changes direction, so the derivative is zero, and from [tex] 0\rightarrow\infty [/tex] the function is increasing so the derivative is positive.
     
  6. Nov 13, 2004 #5
    Although the slope of 2x is postive, the value of the function is negative.

    It is the value of the function which you must be concerned with.
     
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