Question

A gardener uses 144 feet of fencing to build a rectangular garden. The function A(w)=24w−w2 can be used to find the area of the garden for a given width, w. Does the function model the situation over the interval 12

Answer 1

Answer:

The graph of the equation is shown in the picture attached below.

We can see w = 12 corresponds to the global maximum of the function, and for any w greater than 12 the value of A(w) decreases.

This means that for any value of the width greater than 12, the function cannot model the situation.

Making the equation only valid for

w ∈ [0,12]