An enclosed area is designed using one existing wall, and 72m of fence material. What is the maximum area of the enclosure?

The maximum area possible is 648 squared meters.

Step-by-step explanation:

Let the length of the existing wall be .

And let the width of the fence be .

The area of the enclosure will be given by:

Since the area is bounded by one existing wall, the perimeter (the 72 meters of fencing material) will only be:

We want to maximize the area.

From the perimeter, we can subtract 2w from both sides to obtain:

Substituting this for our area formula, we acquire:

This is now a quadratic. Recall that the maximum value of a quadratic always occurs at its vertex.

We can distribute:

Find the vertex of the quadratic. Using the vertex formula, we acquire that:

So, the maximum area is:

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: