MATH110 December 2010
• Q1 (a) • Q1 (b) • Q1 (c) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q6 (c) • Q7 • Q8 (a) • Q8 (b) • Q9 (a) • Q9 (b) • Q9 (c) • Q9 (d) • Q9 (e) • Q9 (f) • Q10 •
Question 09 (d)
Find all critical points of , if they 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!
Recall that the critical points of are those x-values where the derivative is zero or undefined.
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.
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 start by calculating the derivative of , using the quotient rule:
The critical points of the function are the x-values where the derivative is either undefined or equal to zero.
The derivative here is undefined when the denominator is equal to zero. Setting the denominator equal to zero...
...and solving for x, we get that is undefined when .
To find the remaining critical points, we set the derivative equal to zero and try solving for x.
As it turns out, there are no x-values that will satisfy this equation. Thus our only critical point is at .
Click here for similar questions
MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Critical points and intervals of increase and decrease, Pages using DynamicPageList parser function, Pages using DynamicPageList parser tag