Science:Math Exam Resources/Courses/MATH110/April 2019/Question 07 (b)
Work in progress: this question page is incomplete, there might be mistakes in the material you are seeing here.
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q2 (a)(i) • Q2 (a)(ii) • Q2 (a)(iii) • Q2 (b) • Q2 (c) • Q3 • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 • Q7 (a) • Q7 (b) • Q7 (c) • Q8 • Q9 • Q10 (a) • Q10 (b) •
Question 07 (b) 

Using an appropriate quadratic approximation of , find another estimate of . This time you do not need to simplify your answer. 
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 

Given a twicedifferentiable function , its quadratic approximation at a point is a function such that have the same value, slope and second derivative at a. In this case and the point . 
Hint 2 

Once you have the formula for the quadratic approximation of , compare it to the linear approximation you calculated in part (a). Do you notice any similarities? Can you think of how this helps you calculate the quadratic approximation more efficiently in an exam scenario? 
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. We are asked to use the quadratic approximation of at the point to approximate . The formula for this quadratic approximation, which we denote by , is given by . We already know that , so we need only find . To do so, we apply the power rule twice, and find that: , and then Substituting this information into our formula for , we have . Then, to estimate the value of , we plugin into our quadratic approximation. This gives . 