Science:Math Exam Resources/Courses/MATH110/April 2016/Question 08 (c)

MATH110 April 2016

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Question 08 (c)
(c) Sketch a graph to illustrate your claim in part (b). Your sketch must show clearly the graph of the linear function used to compute the approximation in part (a) and how the approximation compares to the exact value of ${\frac {1}{4.16}}$. Your sketch need not be in scale.

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
You should know how to draw the graph of ${\frac {1}{x}}$ for $x>0$. If you forgot, just make sure you know whether the function is increasing/decreasing and make sure you know the concavity.

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. If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work. If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.

Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. You should start by drawing a graph of ${\frac {1}{x}}$. We take the tangent line at the point $(4,{\frac {1}{4}})$. We compare the point $A=(4.16,{\frac {1}{4.16}})$ on the graph of $y={\frac {1}{x}}$ and the point $B=(4.16,0.24)$ on the graph of the tangent line. The linear approximation at point $B$ is seen to be an underestimate.