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 .

Raffaele2014-06-09T05:41:19Z

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

10

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