Science:Math Exam Resources/Courses/MATH104/December 2012/Question 04 (a)
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Question 04 (a) 

The demand equation for a certain product is where q is the number of units per hour the manufacturer can sell at a price of p dollars per unit. Calculate q and when the price is set at $4. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

To calculate you can use implicit differentiation. Alternatively, you can solve for in terms of and then differentiate. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. To determine when is simply a matter of substituting into the demand equation and solving for . We ignore the negative solution since it is not possible to have negative demand. Therefore To determine , we use implicit differentiation. Substituting the values into the expression gives the value of : 
Solution 2 

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Please rate my easiness! It's quick and helps everyone guide their studies. Instead of implicitly differentiating, we first solve the equation for q and then differentiate normally. Then Substituting in gives 