Science:Math Exam Resources/Courses/MATH104/December 2011/Question 02 (e)
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Question 02 (e) 

Consider the function Its first and second derivatives are given by and Find the coordinates of all local maxima, local minima, and inflection points. Be sure to indicate which is which. 
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? 
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Hint 

If a point is a maximum or minimum, what must be true about its derivative? What can be said about the connection between inflection points and the second derivative? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Local Maxima and Minima To find local maxima and minima, we consider critical points which are points where the derivative is zero or does not exist. In part (c), we got that the critical points were In that same part we got that the function was
To find inflection points, we consider where the second derivative is zero or does not exist. In part (d) we got that the second derivative vanished or failed to exist at In that same part we got that the function was
We are asked to get the coordinates and we sub the x values for our maxima, minima, and inflection point into the function to find the y values. Therefore we conclude that
