Science:Math Exam Resources/Courses/MATH104/December 2014/Question 01 (h)
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Question 01 (h) |
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Assume and are differentiable on their domains with . Suppose the equation of the line tangent to the graph of at the point is and the equation of the line tangent to the graph of at is . Find . |
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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Use chain rule. |
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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Please rate my easiness! It's quick and helps everyone guide their studies. By the chain rule we get that , in particular, .
For a differentiable function the slope of the tangent line at a point equals the derivative of the function at that point. The slope of the tangent line of at is , hence . Similarly, .
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