Science:Math Exam Resources/Courses/MATH102/December 2017/Question 04
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Question 04 

Shown below is the graph . You would like to approximate . If you do this using linear approximation centered at , the result will be roughly: A. 2.2 Template:0 B. 2 Template:0 C. 2.1 Template:0 D. 1.8 Template:0 E. 1 Template:0 F. 0.8 Template:0 G. None of these 
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 

The linear approximation of the function at a point is its tangent line at the point. 
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. The linearization at is the tangent line at . From the graph, we see that here the tangent line is horizontal, i.e. . Therefore, at we also get . Answer: . 