Science:Math Exam Resources/Courses/MATH100/December 2018/Question 05 (b)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q5 (d) • Q6 • Q7 • Q8 • Q9 • Q10 • Q11 (a) • Q11 (b) •
Question 05 (b) 

Let (b) Find the and for all the point(s) where has a local minimum or local maximum, clearly indicating which point(s) are local minima and which point(s) are local maxima. 
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 

What are the critical points? Remember to consider value(s) where is undefined as well. 
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.

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 can see from that if and undefined if . We also know is increasing for and decreasing for . Therefore, a local maximum occurs at . Moreover, a local minimum occurs at since is decreasing for and increasing for for . Hence, . 