Science:Math Exam Resources/Courses/MATH104/December 2014/Question 03 (b)
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Question 03 (b) 

The price (in dollars) and the demand for a product are related by the following demand equation: If the current demand is , will the revenue increase or decrease if the price is raised slightly? 
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Hint 

The revenue function is given by . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Substituting in the relation given, we obtain that . Next, we determine the value of when . From the calculation in the above, we know that , substituting yields: . Last, we check what the change in revenue is when . Recall that and hence, using the product rule when differentiating with respect to price, . Substituting , we obtain that . Since when price , slightly raising the price will increase the revenue. 