Question #2c9eb

1 Answer
Feb 7, 2018

#A = 25#

Explanation:

Given: #y = -4x+20#

The area of the rectangle is:

#A = xy#

Substitute #y = -4x+20#:

#A = x(-4x+20)#

#A = -4x^2+20x#

#(dA)/dx = -8x+20#

#(d^2A)/dx^2 = -8#

Because the second derivative is always negative, we know that the x coordinate of the maximum area can be obtained by setting the first derivative equal to 0:

#-8x+20 = 0#

#x = 20/8#

#x = 2.5#

Compute the area at #x = 2.5#

#A = -4(2.5)^2+20(2.5)#

#A = 25#