QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
$\square$ f of $x$ equals, negative 500, $x$ squared, plus $25,000 x$
The revenue $f(x)$, in dollars, that a company receives from sales of a product is given by the function $f$ above, where $x$ is the unit price, in dollars, of the product. The graph of $y=f(x)$ in the $x y$-plane intersects the $x$-axis at 0 and $a$. What does $a$ represent?
A. The revenue, in dollars, when the unit price of the product is $\$ 0$
B. The unit price, in dollars, of the product that will result in maximum revenue
C. The unit price, in dollars, of the product that will result in a revenue of $\$ 0$
D. The maximum revenue, in dollars, that the company can make
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Answer
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Step 1: Identify the given function and its intercepts
The x-axis intercepts can be found by setting $f(x) = 0$ and solving for $x$.
Step 2: Solve for the x-axis intercepts
So, the graph intersects the x-axis at $x = 0$ and $
\begin{align*} f(x) &= 0 \ - 500x^2 + 25000x &= 0 \ \end{align*} x = 50$.
Final Answer
Therefore, the correct answer is option C: The unit price, in dollars, of the product that will result in a revenue of $\$ 1$.
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