Two sides of a rectangle lie along the x and y axes. The vertex opposite the origin is in the first quadrant and lies on 3x+2y = 6. What is the maximum area of the rectangle.
the horizonatal length is x and the vertical length is y. to get y rearrange the eqn to get y = -3x/2 + 3
so the area is x(-3x/2 + 3)
A = -3(x^2)/2 + 3x)
dA/dx = -3x + 3
stat pts at dA/dx = 0
-3x - 3 = 0
x = 1
d2A/dx2 = -3 --> max pt
A = -3/2 + 3
=1.5
