Question

The function A = 15x - x2, where x is the width in yards, gives the area A of a llama pen in square yards. Make a table using 1/2 units from 0 to 10. Graph the function. Use your graph to answer the following question:

Which width gives the greatest area?
Which width gives the greatest area?
a.
6 yd
c.
8.5 yd
b.
7.5 yd
d.
10 yd

Answer 1

The width which gives the greatest area is 7.5 yd

Explanation:

This is an application of differential calculus. Given the area as a function of the width, we simply need to differentiate the function with respect to x and equate to zero which yields; 15-2x=0 since the slope of the graph is zero at the turning points. Solving for x yields, x=7.5 which indeed maximizes the area of the pen