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Math Help - Calculus problem on optimization.

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    Calculus problem on optimization.

    Hi I was wondering if anyone can help with this it just doesn't click with me...

    A 40 cm string is cut in 2. one piece forms a square and the other a circle. find what the lengths of the pieces has to be so that the total of the areas is minimal.
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    Re: Calculus problem on optimization.

    Quote Originally Posted by temporary View Post
    Hi I was wondering if anyone can help with this it just doesn't click with me...

    A 40 cm string is cut in 2. one piece forms a square and the other a circle. find what the lengths of the pieces has to be so that the total of the areas is minimal.
    let one piece of string have length x ... other piece will have length 40-x

    let x = piece forming a circle

    x = 2\pi r , derive an expression for the circle area in terms of x

    40-x = piece forming a square

    40-x = Perimeter of the square , derive an expression for the square area in terms of x

    total area, A = circle area as a function of x + square area as a function of x

    find \frac{dA}{dx} and determine the value of x that minimizes the total area
    Thanks from HallsofIvy
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