Question

Simon has 160160160 meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width xxx (in meters) is modeled by A(x)=-x(x-80)A(x)=−x(x−80)A, left parenthesis, x, right parenthesis, equals, minus, x, left parenthesis, x, minus, 80, right parenthesis What width will produce the maximum garden area?

Answer 1

Answer:

40 metres

Step-by-step explanation:

Given the garden's area (in square meters) as a function of the garden's width x (in meters) modeled by the equation A(x)=−x(x−80), the width that will produce the maximum garden area will occue at dA(x)/dx = 0

Given A(x)=−x(x−80)

A(x) = -x²+80x

dA(x)/dx = -2x+80

-2x+80 = 0

-2x = -80

Dividing both sides by -2

-2x/-2 = -80/-2

x = 40 metres

Hence the width that will produce the maximum garden area is 40 metres