a rectangle has its base on the x-axis & its upper 2 vetices on the parabola y=12-x^2. wat is the largest area

Question

the rrectangle can have and wat are the dimension??

Answer 1

Ok, I have the idea right now :

First, graph the parabola, it's not that difficult, just look for the vertex and the intercepts :

y = 12 - x^2

for y = 0 ; x = +/-sqrt(12)

for x = 0 ; y = 12

the parabola is pointing from up to down, ok.

the base = 2x

the height = b

area = 2x*b

x and b are points of the parabola :

12 - x^2 = b

area = 2x(12 - x^2) = 24x - 2x^3

dA / dx = 24 - 6x^2 = 0

x = +/-2 >>> critical points

let's choose : x = 2

so : base = 2x = 4

height = 8

maximun area = 4*8 = 32

hope that might help you

Answer 2

W = 2x, L = y = 12 - x^2
Area of the rectangle = 2x * y = 24x - 2 x^3
dA/dx = 24 - 6 x^2
x^2 = 4
x = +/- 2
y = 8

W = 4, L = 8, A = 32