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Math Help - The connection between partial derivates and slopes...

  1. #1
    Junior Member
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    The connection between partial derivates and slopes...

    My Calculus book is just going on about derivations to formulas so I would need help with this question:

    An area on a map is provided with rectangular xy-coordinates. The height over the ocean is given by the function h(x,y). If h'x(a,b)=0.1 and h'y(a,b)= -0.2 what could be said about the ground at the point (a,b), ie what is its slope?

    I know how to calculate partial derivatives but I dont really understand their purpose or the answer to the above stated question.

    Help would be muchos appreciated!
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  2. #2
    Senior Member
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    Mar 2009
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    You are probably confused, because what does slope mean in two dimensions? Maybe read about gradients.

    It should be clear to you that the slope in the x-direction (a,b) is 0.1 and the slope in the y-direction at (a,b) is -0.2, since this is what derivatives are all about. Maybe this is what the question was asking?
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