Science:Math Exam Resources/Courses/MATH110/April 2018/Question 03 (b)
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Question 03 (b) 

For what value of the constant does the graph of have a horizontal tangent line at ? 
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Hint 

The graph of a function has a horizontal tangent line at if . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let . Then the graph of has a horizontal tangent line at if . The first step is to calculate with the indeterminate constant . Using the product rule, we get So at , we have .
Now we have to solve the equation for . Noting that is never zero (in fact, it is always positive), we can divide both sides by , which leaves . It follows that . Answer: The graph of has a horizontal tangent line at if and only if . 