Science:Math Exam Resources/Courses/MATH104/December 2010/Question 02 (a)
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Question 02 (a) 

Find an equation of the tangent line to the curve at the point (1,2) on the curve. Please simplify. 
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 

What is the slope of the tangent line? Do you know one point that the tangent line passes through? 
Hint 2 

The slope of the tangent line is the derivative of with respect to , evaluated at and Use implicit differentiation to find 
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. To find the slope of the tangent line, we consider as a function of near the point (1,2) and use implicit differentiation to find : Isolating , Hence, The slope of the tangent line to the curve at is then Since the tangent line passes through the point and has slope , its equation is 