Science:Math Exam Resources/Courses/MATH100/December 2012/Question 02 (b)
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Question 02 (b) 

ShortAnswer Questions. Questions 14 are shortanswer questions. Put your answers in the boxes provided. Simplify your answers as much as possible, and show your work. Each question is worth 3 marks, but not all questions are of equal difficulty.

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 the relationship between slopes of tangent lines and derivatives. 
Hint 2 

Implicitly differentiate with respect to x and then plug in . Solve for to get the slope since the derivative at a point is equal to the slope of the tangent line to the curve at that point. 
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. Implicitly differentiating gives
Plugging in gives
completing the question. 