Science:Math Exam Resources/Courses/MATH100/December 2016/Question 09 (b) (ii)
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Question 09 (b) (ii) 

Let . (ii) Find all intervals where is increasing. 
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Hint 

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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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. 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 . 