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

FullSolution Problems. In questions 28, justify your answers and show all your work. Simplification of answers is not required unless explicitly stated. Let Find the critical numbers of y = ƒ(x). 
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 

Critical points (numbers) are roots of the derivative. 
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 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. Critical points (numbers) are roots of the derivative. Let's compute this derivative: And now find the roots: We can divide by 6/5 Now, clearly x = 0 is a solution. To find possibly others, we now assume that x isn't zero and now multiply by x^{4/5} And obtain a second solution. So we can conclude that there are two critical points: x = 0 and x = 1. 
Solution 2 

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Please rate my easiness! It's quick and helps everyone guide their studies. Critical points (numbers) are roots of the derivative. Let's compute this derivative: And now we can do a little algebra on the function and rewrite as And so the critical points are solutions of either or And so we have two critical points: x = 0 and x = 1. 