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Math Help - Calculus Problem - Optimization

  1. #1
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    George
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    Calculus Problem - Optimization

    Hi i was wondering if anyone could help me with this calculus optimization problem i know how to do most optimization problems but this one stumps me.

    Some lines through the point (2,1) cut off a triangle in the 1st quadrant. Find the x - intercept of the line with the property that the sum of its x and y intercepts is a minimum.

    *What i know so far is that the equation of any line is y = mx + b
    *The x intercept would be when y = 0 so 0 = mx + b
    *The y intercept would be when x = 0 so y = b essentially
    *I am not sure if this would be true but the equation of any line on that point would be 1 = 2m + b

    I am not sure what to do from this point.

    Help would be greatly appreciated
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  2. #2
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    Re: Calculus Problem - Optimization

    if i find the y intercept it would be y = b
    if i find the x intercept it would be x = -b/m
    so the sum would be b - (b/m)
    which still doesnt make sense do i solve for m in the other equation?
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  3. #3
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    Re: Calculus Problem - Optimization

    the line through (2,1) has equation ...

    y - 1 = m(x - 2)

    the y-intercept is y_0 = -2m+1

    the x-intercept is x_0 = 2 - \frac{1}{m}

    the sum of the intercepts is ...

    S = -2m + 3 - \frac{1}{m}

    Determine the value of the slope m (remember it must be negative) that minimizes the sum, S ... then find the x-intercept.
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  4. #4
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    Re: Calculus Problem - Optimization

    thank you so much skeeter
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