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Math Help - Does the antiderivative of a function gives any information about it's graph?

  1. #1
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    Does the antiderivative of a function gives any information about it's graph?

    This question may look a little obvious but here we go:

    In every Calculus 1 course we learn that using a function's firth and second derivatives we can know a lot of things about it's graph.
    But if we only have an antiderivative of a function( \int { f(x)dx=x({ x }^{ 3 } } +1) for example) can we know anything about it's graph before differentiating?
    I guess that could it be something like \Delta x, since the classic Galileo equation for uniform acceleration \Delta x={ x }_{ 0 }+{ v }_{ 0 }\Delta t+\frac { 1 }{ 2 } a{ \left( \Delta t \right)  }^{ 2 }.

    Thanks for answering
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  2. #2
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    Re: Does the antiderivative of a function gives any information about it's graph?

    I presume that you have learned that the anti-derivative (integral) gives the area under the curve.
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