Science:Math Exam Resources/Courses/MATH110/December 2010/Question 04 (a)
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Question 04 (a) 

Given a differentiable function , recall that there are two definitions for : and Pick one of these definitions and draw a picture to illustrate the fact that the limit on the righthand side is the limit of slopes of secant lines. Make sure to include the labels and . 
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 

Draw an a and x (or an x and an x + h) on the xaxis. Given a drawing of a function , what are the corresponding labels on the yaxis? 
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. A drawing illustrating the first definition given would look something like this: See as , the slope of the line between and approaches the slope of the tangent line 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. A drawing illustrating the first definition given would look something like this: As , the slope of the line between and approaches the slope of the tangent line at . 