Science:Math Exam Resources/Courses/MATH110/April 2017/Question 02 (a)
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Question 02 (a) |
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For the curve defined by the equation , find the slope of the tangent line 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 |
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Here, you want to compute the derivative of y, but it is annoying to solve for y and then compute the derivative. In this situation, it is better to use implicit differentiation to compute the derivative. |
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.
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Solution |
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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 have the equation
We want to use implicit differentiation to find . We take the derivative of both sides:
Now, we solve for :
And now, we plug in and . We know that and , so we get
Answer: |