Science:Math Exam Resources/Courses/MATH102/December 2011/Question 01 (b) i
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Question 01 (b) i 

ShortAnswer Questions. A correct answer in the box gives full marks. For partial marks work needs to be shown. Consider the curve Find at the point x = 0. 
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 

You can either use implicit differentiation or solve for y. Give it a try, we provide a solution for each method. 
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 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. To do this problem, we rearrange the equation to isolate and then take the derivative of with respect to : Using the quotient rule, we evaluate and we are done: Hence, at x = 0 we obtain 
Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. We can also use implicit differentiation. By differentiating with respect to x we obtain: (Watch out for the product rule on the term y(1x)) The difference is that we need to know the value of y when x = 0, but if we plug that in the original equation we obtain and so we have that y = 0. We use this in what we obtained by differentiating implicitly: and so we have that 