Science:Math Exam Resources/Courses/MATH100/December 2011/Question 05 (b)
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Question 05 (b) 

FullSolution Problems. In questions 28, justify your answers and show all your work. Simplification of answers is not required unless explicitly stated. Let

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 

Derivatives can help us detect where functions are decreasing. Try determining when the derivative is negative. 
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 

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Please rate my easiness! It's quick and helps everyone guide their studies. The intervals of decrease are the intervals on which the derivative of the function ƒ is negative. Given that Our critical points occur when , that is, points on the function where the derivative is undefined or zero. Writing out a sign chart, we see that when we have that . When we have that . When we have that . Hence the function is decreasing on . 