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Math Help - Homework Help

  1. #1
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    Homework Help

    Can some one please tell me what f'(a) times deltaX means? Does it represent a length, a slope, or an area? What about f(a) times deltaX?

    Thanks to anyone who can help me with these questions!

    -M
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  2. #2
    MHF Contributor
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    Quote Originally Posted by blurain View Post
    Can some one please tell me what f'(a) times deltaX means? Does it represent a length, a slope, or an area? What about f(a) times deltaX?

    Thanks to anyone who can help me with these questions!

    -M
    deltaX is a small displacement along the x-axis.

    f'(a) is the slope of the function at x=a.

    f'(a)*deltaX can be understood to be the displacement of the function given the small displacement of x.

    f(a) is the value of the function at x = a.

    f(a)*deltaX can be understood to be, with a measurable error, the area under the curve - a tiny rectangle with base deltaX and height f(a).

    It is when deltaX shinks that things get REALLY interesting.
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