A rectangle is bounded by the x-axis, the y-axis, and the line y = (4-x)/4. Find the maximum area of such a rectangle.

Answer 1

let the point on the line be (x,y)
line is y = (4-x)/4 = 1 - (1/4)x

area of rectangle:
A = xy
= x( 1 - (1/4)x)
= x - (1/4)x^2

this is a downwards parabola. We need the vertex

the x of the vertex is -b/2a = -1/(-1/2) = 2
then y = 1- (1/4)(2) = 1/2

max area = xy = 2(1/2) = 1

check my arithmetic

Answer 2

Thank you so much!