MATH104 December 2011
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q1 (j) • Q1 (k) • Q1 (l) • Q1 (m) • Q1 (n) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q2 (e) • Q2 (f) • Q2 (g) • Q3 • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q5 (d) • Q6 (a) • Q6 (b) • Q6 (c) • Q6 (d) • Q6 (e) •
Question 02 (b)
|
Consider the function
Its first and second derivatives are given by
and
Find all such that or does not exist.
|
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
|
Try setting the numerator and the denominator to 0. What does a value of 0 in the numerator correspond to? How about when the denominator is 0?
|
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.
To determine where f"(x)=0, we look at the numerator of f"(x) and note that f"(x)=0 when the numerator is zero, i.e.
Since x2+9=0 has no real solutions, the only value of x that satisfies the above equation is when x=0.
To determine where f"(x) does not exist, we set the denominator to 0, i.e.
So, f"(x) does not exist when .
Remark: Note that the denominator and numerator are never simultaneously 0. If they were, say at x=a, we would have to take the limit of f"(x) as to determine if f"(x) did not exist or was zero (or another finite number).
|
Click here for similar questions
MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Function properties, Pages using DynamicPageList3 parser function, Pages using DynamicPageList3 parser tag
|
Math Learning Centre
- A space to study math together.
- Free math graduate and undergraduate TA support.
- Mon - Fri: 12 pm - 5 pm in LSK 301&302 and 5 pm - 7 pm online.
Private tutor
|