Science:Math Exam Resources/Courses/MATH110/December 2014/Question 06 (c)
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Question 06 (c) 

This question has three independent parts. (c) Find the equation of the tangent line to the curve at the point . 
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 

Recall the tangent line formula: a tangent line of a function at a point is given by

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 

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Please rate my easiness! It's quick and helps everyone guide their studies. By the tangent line formula in the Hint, the tangent line of at is given by . Therefore, it is enough to find and . Using , we can easily obtain . On the other hand, by the product rule, we have the derivative of as , so that . Collecting the terms, we finally get the desired tangent line as 