Science:Math Exam Resources/Courses/MATH100/December 2018/Question 01 (c)
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Question 01 (c) 

Find an equation for the tangent line to the curve when . 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Recall that for a function , the tangent line to at the point is given by the equation . 
Hint 2 

Use the equation from Hint 1 with and . 
Hint 3 

To find , use the chain rule. 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. Let , then the tangent line at will be given by the equation . Using the chain rule, we get , and therefore . Plugging this and into the equation for the tangent line gives . After rearranging, we conclude that the tangent line is . 