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Prism
Prism asked in Science & MathematicsMathematics · 7 years ago

find the value of x for which the perimeter is a maximum?

the perimeter of a shape is given by p= sqrt(2x-x^2) where x is the length of one side.

find the value of x for which the perimeter is a maximum.

The word maximum totally confuses me please explain this and also help with works and solutionss thank .

1 Answer

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  • Raffaele
    Lv 7
    7 years ago

    p= √(2x - x^2)

    differentiate wrt x

    p ' = (1 - x)/√(x (2 - x))

    maximum is achieved at x = 1

    because p ' = 0 and p' > 0 for x < 1 and p' < 0 for x > 1

    which means that the function increases until x = 1 then decreases

    so x = 1 is proven to be a maximum

    and maximum perimeter is

    p(1) = 1

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