Science:Math Exam Resources/Courses/MATH100/December 2015/Question 10 (g)/Solution 1

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We need to determine the sign of.

From part (e) we have , where is always positive so it doesn't have any role in the sign. We only need to determine the sign of .

From part (f) is at ,

so we make a sign chart for to find where it is positive and negative and therefore where the function is increasing and decreasing.

decreasing increasing decreasing

Intervals that is decreasing: .

Intervals that is increasing: .