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Math Help - Help me with some calculus questions.. i couldn't go through..

  1. #1
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    Help me with some calculus questions.. i couldn't go through..

    Help me with some calculus questions which I couldn't go through...

    a) Find the intervals on which function is increasing and decreasing ?
    f(x) = x^3 - 3x^2

    b) Find the intervals on which function is increasing and decreasing ?
    f(x) = 1 / x^2


    c) what are critical numbers for:
    i) f(x) = x^3 - 3x^2 and
    ii) f(x) = 3x^4 - 4x^3

    d) For which interval the function f(x) = 8x^3 - 2x^4 is concave downwards?

    e) Find the points of inflection for f(x) = x^4 - x^3 ...
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  2. #2
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    Quote Originally Posted by khai View Post
    Help me with some calculus questions which I couldn't go through...

    a) Find the intervals on which function is increasing and decreasing ?
    function is increasing on \frac{dy}{dx}>0

    function is decreasing on \frac{dy}{dx}<0

    that any help?
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  3. #3
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    Quote Originally Posted by khai View Post
    c) what are critical numbers for:
    i) f(x) = x^3 - 3x^2 and
    ii) f(x) = 3x^4 - 4x^3
    Find the first derivative of your function, set the equal to zero and solve for x. Those are your critical points.

    d) For which interval the function f(x) = 8x^3 - 2x^4 is concave downwards?

    e) Find the points of inflection for f(x) = x^4 - x^3 ...
    The function is concave down when f''(x)<0 for all values of x on a given interval. When the function changes concavity you have your inflection points.
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