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

ShortAnswer Questions. A correct answer in the box gives full marks. For partial marks work needs to be shown.
a. Based on the above table, provide the best estimate for f(x) and fill in the second table.
b. Estimate 
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 

Remember that the derivative is the slope of the tangent line of a function at a point on the function. What would be a good way to estimate this line? Try drawing a picture to give you an idea. 
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  

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Please rate my easiness! It's quick and helps everyone guide their studies. Given the data we have, the best way to approximate the derivative is by using secant lines! For an example, let's first estimate . For this, lets use the secant line from x=1 and x=1.5. This gives . Proceeding as above, we can fill in the table as follows:
For the second derivative, we use the same logic above except we do it with the derivative as our function. This gives
and this completes the question. 