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Thread: Geometrical Application of Differentiation

  1. #1
    Senior Member
    Jul 2008

    Exclamation Geometrical Application of Differentiation

    Hey guys

    A window frame has the shape of a rectangle surmounted by a semi-circle. The perimeter of the frame is constant. Show that, for max. area, the height of the rectangle is equal to the radius of the semi-circle.

    Could someone please show me how to do this question?

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  2. #2
    Junior Member
    Mar 2009
    Ok, I took the time to work through this problem and got the solution. I don't want to just blurt out the steps and answers for ya, but I can hopefully point your way to understanding how to solve these kinds of things.

    First, you need to work out some equations for the problem. You have two equations you can put together from that info. You know an equation for the perimeter, and for the area. So first, find those.

    Just to get you on the path after that, this is a maximization problem, so you want to take the derivative of your two equations. For example, finding dA / dr (derivative of A (area) with respect to r (the radius). But take care with h (the height of the rectangle) that should be in the equations! If you've done implicit differentiation, then you should know how to handle this.

    Can you figure it out after this, as well?

    If you get stuck again, let me know and I'll coach you through to the end.
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