Science:Math Exam Resources/Courses/MATH110/December 2016/Question 07 (d)
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Question 07 (d) 

Consider the function . (d) Explain why there are no points on the curve where the tangent line has slope . 
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Hint 

Recall that for any real number . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Recall that the slope of the tangent line is the derivative of the function. By part (c), if , then Rearranging, However, for any . Thus, the above equation has no solution. In other words, there does not exist a value so that .
Answer: 