Question
The supply function for a certain make of satellite radio is given by$$p=f(x)=0.0001 x^{5 / 4}+10$$where $x$ is the quantity supplied and $p$ is the unit price in dollars.a. Find $f^{\prime}(x)$b. What is the rate of change of the unit price if the quantity supplied is 10,000 satellite radios?
Step 1
The supply function is given by: \[ p = f(x) = 0.0001 x^{5/4} + 10 \] Show more…
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Supply Function for Satellite Radios The supply function for a certain make of satellite radio is given by $$ p=f(x)=0.0001 x^{5 / 4}+10 $$ where $x$ is the quantity supplied and $p$ is the unit price in dollars. a. Find $f^{\prime}(x)$ b. What is the rate of change of the unit price if the quantity supplied is 10,000 satellite radios?
Differentiation
Basic Rules of Differentiation
The supply equation for a certain brand of radio is given by $$p=s(x)=0.3 \sqrt{x}+10$$ where $x$ is the quantity supplied and $p$ is the unit price in dollars. Use differentials to approximate the change in price when the quantity supplied is increased from 10,000 units to 10,500 units.
Differentials
Suppliers of satellite radios will market 10,000 units when the unit price is $20$dollar and 62,500 units when the unit price is $35$dollar. Determine the supply function if it is known to have the form $$p=a \sqrt{x}+b \quad(a>0, b>0)$$ where $x$ is the quantity supplied and $p$ is the unit price in dollars. Sketch the graph of the supply function. What unit price will induce the supplier to make 40,000 satellite radios available in the marketplace?
Functions, Limits, and the Derivative
Functions and Mathematical Models
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