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Math Help - Sketching cubic function to calculate area under the curve by integration

  1. #1
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    Sketching cubic function to calculate area under the curve by integration

    Hi,
    The question asks us the sketch the curve of y= 3x^3-10 for x E [2,4].

    i've tried the usual way of finding interepts. For the y intercept i get the point (0,-10). The x intercept gives me x^3=10/3 which doesn't seem to help me for sketching purposes.

    I then tried to find max and mins but when i let dy/dx = I keep getting the same coordinates as for the y intercept. Also tried getting point of inflection but get the same point again. Should I just sub in values for x and get their corresponding y values?
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  2. #2
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    Re: Sketching cubic function to calculate area under the curve by integration

    quite hard to help you without just telling you the answer. do you know what y=x^3 looks like?

    if you are on a basic course...you could just substitute values of x (say 2,2.5,3,3.5,4) into the function and plot the values.
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  3. #3
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    Re: Sketching cubic function to calculate area under the curve by integration

    Because your question is interested in the particular interval [2,4] , your critical points are x = 2, x=4 and value of x where the d/dy equals 0. The only place d/dy equals zero is at the point x=0, whcih is not in your interval.
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