Answer:
Step-by-step explanation:
For this case we assume that the total perimeter is 18 ft, we have a wall and the two sides perpendicular to the wall measure x units each one so then the side above measure P-2x= 18-2x.
And we are interested about the maximum area.
For this case since we have a recatangular area we know that the area is given by:
Where L is the length and W the width, if we replace from the values on the figure we got:
And as we can see we have a quadratic function for the area, in order to maximize this function we can use derivates.
If we find the first derivate respect to x we got:
We set this equal to 0 in order to find the critical points and for this case we got:
And if we solve for x we got:
We can calculate the second derivate for A(x) and we got:
And since the second derivate is negative then the value for x would represent a maximum.
Then since we have the value for x we can solve for the other side like this:
And then since we have the two values we can find the maximum area like this:
