Science:Math Exam Resources/Courses/MATH104/December 2013/Question 01 (m)
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Question 01 (m) 

Let be a differentiable function such that and If the tangent line to the graph of at is used to approximate , then the approximate solution for to the equation is (A) . (B) . (C) . (D) . (E) . 
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 

First, we find the equation of the tangent line. Remember that the derivative at a point gives you the slope of the tangent line. 
Hint 2 

Once you have the tangent line, use it to approximate . Thus, we have
where we find by plugging in the point into . Then set the above equation to 0 and solve for . 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. To see this, notice that the equation of the line using the point slope formula is given by . Isolating gives
and simplifying one last time . We are using this line to approximate . Thus, if we set and solve, we can get an approximation to the root of . Hence, set which gives . Thus the correct answer is (C). 