Application of Calculus

If $R(x) = 8x - x^2$, find the value of $AR$ at $x=4$.

If $C(x) = x^2 + 4$, what is the Marginal Cost at $x=3$?

The Marginal Cost function is the _____ of the Total Cost function.

If the profit function is $P(x) = 50x - 2x^2$, find the marginal profit function.

If $R(x) = 15x$, the average revenue is:

For $C(x) = 3x^2 + 2x + 1$, the marginal cost function is:

Given the total cost function $C(x) = 2x^2 + x + 5$, what is the marginal cost at a production level of $x = 100$ units?

If the demand function for a certain commodity is given by $p = 30 - x$, find the marginal revenue when $x = 10$.

The total revenue received from the sale of $x$ units of a product is given by $R(x) = 3x^2 + 36x + 5$. What is the marginal revenue when $x = 5$?

If the average cost function of a product is $AC = 5 + \frac{100}{x}$ and the average revenue is $AR = 10$, what is the break-even quantity $x$?

If $P(x)$ represents the profit function of a firm, then the break-even point occurs when:

The total revenue function of a product is $R(x) = 15x$ and the total cost function is $C(x) = 500 + 10x$. Find the break-even quantity $x$.