Science:Math Exam Resources/Courses/MATH100/December 2013/Question 06
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Question 06 

FullSolution Problem. Justify your answer and show your work. Full simplification of numerical answers is required unless explicitly stated otherwise. Using the definition of the derivative, compute if . No marks will be given for the use of differential rules, but you may use them to check your answer. 
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 

The derivative of at is the slope of the line tangent to at . What is the expression for the slope of a line? 
Hint 2 

The slope of a line between two points and is . What happens as ? How can we express this mathematically? 
Hint 3 

The limit definition of the derivative of at is . 
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 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. By the limit definition of the derivative of at ,

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. By the alternative limit definition of the derivative of at ,
