Height: 4 units
Width 2√/2
Explanation:
Start by sketching y = 6 - ². Then draw a rectangle beneath it. You will notice that the width is 2x and the height is 6 ². Area is given by length - times width, so the area function will be A=2x (6 - x²) = 12x - 2x³.
Now you differentiate to find the maximum.
A' = 12 - 6x²
Find critical numbers by setting A' to 0.
x = ± √/2
The derivative is negative at x = 2 and positive at x = 1, which justifies that the rectangle with width of √2 has maximal area.
The height will be y (√2) = 6 – (√2)²) = 4
