MATH100 December 2016
• Q1 (a) • Q1 (b) • Q1 (c) • Q2 (a) • Q2 (c) • Q2 (d) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 (a) • Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q8 • Q9 (a) (i) • Q9 (a) (ii) • Q9 (a) (iii) • Q9 (b) (i) • Q9 (b) (ii) • Q9 (b) (iii) • Q9 (c) (i) • Q9 (c) (ii) • Q9 (c) (iii) • Q10 (a) • Q10 (b) • Q11 (a) • Q11 (b) • Q12 • Q13 (a) • Q13 (b) • Q14 (a) • Q14 (b) • Q2 (b) •
Question 09 (b) (ii)
(ii) Find all intervals where is increasing.
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?
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is increasing on if on the interval.
Be careful that the function must be defined at the intervals that you choose for monotonicity.
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From part (i), we have
Note that the function is defined when and and its derivative is defined when and .
This implies that on the domain of , we have
so the sign of is determined by the sign of .
Indeed, we have when and when However, we note that is defined on and is defined on Therefore, is increasing on .