Question

A farmer uses 36 feet of fencing to build a rectangular rabbit pen. The function A(w)=18w−w2 can be used to find the area of the pen for a given width, w.

The farmer finds that the average rate of change over the interval w=3 to w=9 is 6.

What does this mean in terms of the dimensions of the rabbit pen?

Answer 1

9514 1404 393

Answer:

upper right

Explanation:

The rate of change when the dependent variable is area and the independent variable is width is the ratio area/width. An average rate of change of 6 means the area will increase by 6 when the width increases by 1.

a 1 foot increase in width gives a 6 square foot increase in area