Marginal revenue

The weekly demand for Math-Hero video games is given by

where $x$ is the number of video games produced and sold, and $p$ is in dollars. Using the marginal revenue function, $R^{\prime }(x)$, approximate the marginal revenue when 10 Math-Hero video games have been produced and sold and interpret the result.

Marginal revenue

The weekly demand for Math Wars - Return of the Calculus video games is given by

where $x$ is the number thousands of video games produced and sold, and $p$ is in dollars.

Using the marginal revenue function, $R^{\prime }(x)$, approximate the marginal revenue when 10,000 video games have been produced and sold and interpret the result.

Marginal average cost

The daily cost (in dollars) of producing LCD ultra-high definition televisions is given by

where $x$ denotes the number of thousands of televisions produced in a day.

Using the marginal average cost function, ${\bar{C}}^{\prime }(x)$, approximate the marginal average cost when 5000 televisions have been produced and interpret the result.

Elasticity of demand

Given the demand equation $p+{\displaystyle \frac{x}{5}}=40$, where $p$ represents the price in dollars and $x$ the number of units, determine the elasticity of demand when the price $p$ is equal to $20 and interpret the result.

Elasticity of demand

The demand for a product is given by

Determine the elasticity when $p=3$ and interpret the result.

Unitary demand

Given the demand equation $p=12-{\displaystyle \frac{x^2}{25}}$, determine the price $p$ at which demand is unitary.

Maximum revenue

Given the demand equation $p+5x=20$, determine the price $p$ at which total revenue is maximized.