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Homework Help: A question about derivative

  1. Jun 17, 2009 #1
    Hello everyone,

    This is not exactly my homework question. I was looking at the assignments on MIT open courseware page for Single variable calculus and came across this one:

    Problem statement
    Quirk is a flat planet. On the planet Quirk, a cell phone tower is a 100-foot pole on top of a green mound 1000 feet tall whose outline is described by the parabolic equation y = 1000 − x2. An ant climbs up the mound starting from ground level (y = 0). At what height y does the ant begin to see the tower?

    2. Relevant equations

    I guess I will need the derivative at some point: f'(x) = -2x. So, it has a negative slope.

    3. The attempt at a solution
    I am having trouble visualizing the problem. So, the curve meets the y axes at height 1000 and the pole is another 100 feet, so I have a line from (0, 1100) which will meet the curve at some point P. I have to find this point P. Is that correct?

    I guess I will need to find the slope of this line but I am having trouble seeing how this could connect to the slope of the tangent line to the parabola at point P.

    Thanks for any help you can give me.

  2. jcsd
  3. Jun 17, 2009 #2


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    Science Advisor
    Homework Helper

    The coordinates of the point P will be (x,1000-x^2) for some x, right? Call Q the point at the top of the cell tower (0,1100). You want the line through PQ to be tangent to the parabola. The slope of the tangent is -2x. Set that equal to the slope you get from m=delta(y)/delta(x) using the points P and Q and solve for x.
  4. Jun 17, 2009 #3
    Thanks for your reply Dick. This is the bit that I had completely missed that this line would be tangent to the parabola.

    Many thanks,

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