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Math Help - Finding a point P on a curve y=x^3

  1. #1
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    Finding a point P on a curve y=x^3

    The question I have been struggling with is

    Find P on the curve y-x^3 such that the slope of the line passing through P and (1,1) is 3/4
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  2. #2
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    Re: Finding a point P on a curve y=x^3

    Recall the slope of a line can be determined by \frac{y_2-y_1}{x_2-x_1}

    In your case, solve for x such that \frac{3}{4} = \frac{x^3-1}{x-1}
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  3. #3
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    Re: Finding a point P on a curve y=x^3

    Another way of doing this: a line passing through (1, 1) with slope 3/4 is of the form y- 1= (3/4)(x- 1) or y= (3/4)x+ 1/4. Solve that and y= x^3 simultaneously. Just replacing y in y= x^3 with (3/4)x+ 1/4 gives a cubic equation with a simple answer.
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