Science:Math Exam Resources/Courses/MATH104/December 2012/Question 01 (m)
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Question 01 (m) 

On what intervals is the function increasing? Decreasing? 
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 

To determine the interval(s) where a function is increasing, we must search for the values of where the derivative of has what quality? What about for intervals where the function is decreasing? 
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. To determine the values of where is increasing, we must solve for the critical points of and examine the sign of the derivative in between the critical points, solving gives Since the exponential function is never zero for any value of , we can solve the above equation by solving Now we need to evaluate the sign of in the intervals . Taking test points and plugging them into gives: So is positive on and negative on . Therefore, is increasing for , and decreasing for . 