THE AMOUNT OF CLOTH USED TO MAKE FOUR CURTAINS IS GIVEN BY THE FUNCTION A=-4X^2 + 40X WHERE X IS THE WIDTH OF ONE CURTAIN IN FEET AND a IS THE TOTAL AREA IN SQUARE FEET. FIND THE WIDTH THAT MAXIMIZES THE AREA OF THE CURTAINS. WHAT IS THE MAXIMUM AREA?

Answer 1

this problem consists of finding the vertex of the parabola,
the x of the vertex is -b/(2a) = -40/-8 = 5
when x = 5
A = -4(25) + 40(5) = 100

So the maximum area is 100 ft^2 , when the width is 5 ft.

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Answer 2

A=-4x^2+40x
By completing the square
A= -4(x^2-10x+25)+100
A= -4(x-5)^2+100

Vertex is (5,100)
Max is 100 ft

Answer 3

I do not know