A local gym sells monthly memberships. The function f(x) = −x2 + 18x − 72 models the daily profit in dollars, where x is the number of memberships sold.

Question

A local gym sells monthly memberships. The function f(x) = −x2 + 18x − 72 models the daily profit in dollars, where x is the number of memberships sold.

Determine the zeros, and explain what these values mean in the context of the problem.

x = 9, x = 18; The zeros represent the number of monthly memberships that produces a maximum profit.
x = 9, x = 18; The zeros represent the number of monthly memberships when no profit is made.
x = 6, x = 12; The zeros represent the number of monthly memberships that produces a maximum profit.
x = 6, x = 12; The zeros represent the number of monthly memberships when no profit is made.

Answer 1

The correct answer is: x = 9, x = 18; The zeros represent the number of monthly memberships that produces a maximum profit.

In this context, the zeros of the function represent the number of monthly memberships sold that will maximize the profit for the gym. These values indicate that when the gym sells 9 memberships or 18 memberships, it will generate the highest profit. This is because the function reaches its maximum value at these points before decreasing again.