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Math Help - Change of y vs dy?

  1. #1
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    Change of y vs dy?

    Q: Let y = 4 x^2.
    Find the change in y, \Delta y when x= 4 and \Delta x = 0.2
    Find the differential dy when x= 4 and dx = 0.2

    My solution:

    dy/dx = 8x
    dy = 8x * dx
    dy = (8*4)(.2) = 6.4

    But 6.4 is the correct answer only for dy and not change of y, ain't they the same thing?
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  2. #2
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    Quote Originally Posted by tttcomrader
    Q: Let y = 4 x^2.
    Find the change in y, \Delta y when x= 4 and \Delta x = 0.2
    Find the differential dy when x= 4 and dx = 0.2

    My solution:

    dy/dx = 8x
    dy = 8x * dx
    dy = (8*4)(.2) = 6.4

    But 6.4 is the correct answer only for dy and not change of y, ain't they the same thing?
    You know that, dy=f'(x)dx
    At x=2 and dx=.2
    You have,
    dy=f'(4)(.2)
    That is,
    dy=8\cdot 4\cdot .2=6.4
    So the answer is correct,
    ----
    As I understand you question about dy and \Delta y. Consider a smooth graph with a tangent at a point. You move a certain distance from the point. Two things happen, the change in the function which is \Delta y and the change in the tangent line dy, the smaller the change in x or dx the closer dy is to \Delta x. Because if you look at the tangent line you see that it is almost the same value as the curve itself for small distances. As if to say, the tangent consideres the curve as a line on an interval.
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