Awire 24inches long is to be cut into four pieces to form a rectangle whose shortest side has a length of x:
determine the domain of the function and use a graphing utility to graph the function over that domain
use the graph of the function to approximate the maximum area of the rectangle. make a conjecture about the dimensions that yield a maximum area.

Area function :

Domain: (0,6)

The area of rectangle is maximum at x=6. The area of a rectangle is maximum if it is a square.

Step-by-step explanation:

It is given that the length of wire is 24 inches. It is to be cut into four pieces to form a rectangle.

Let x be the length of shortest side.

Perimeter of a rectangle is

Perimeter = 2( Shortest side + longest side).

So, length of longest side is (12-x) inches.

Area of a rectangle is

Area function is

The area of rectangle and dimensions of a rectangle can not be a negative.

It means,

One side is less that the other side.

It means the domain of the function is (0,6).

The simplified form of the area function is

Differentiate with respect to x.

Differentiate A'(x) with respect to x.

Therefore the area of rectangle is maximum at x=6.

It means the area of a rectangle is maximum if it is a square.

The answer is C. If you plug into 6 and -4 together, you will get -24. And add 5, you get -19. Since -19 is further away from zero, it is less than the number that is above them such as -5 and -3. And -8 is closer to zero, it’s greater than any other number to the left like -10 and -20. So, -8 is greater than -19. That’s how you got C.