Science:Math Exam Resources/Courses/MATH102/December 2011/Question 04 (iii)
• Q1 (a) i • Q1 (a) ii • Q1 (b) i • Q1 (b) ii • Q1 (b) iii • Q1 (c) • Q2 (a) i • Q2 (a) ii • Q2 (a) iii • Q2 (b) i • Q2 (b) ii • Q2 (b) iii • Q2 (c) • Q3 • Q4 (i) • Q4 (ii) • Q4 (iii) • Q4 (iv) • Q4 (v) • Q4 (vi) • Q5 • Q6 • Q7 (i) • Q7 (ii) • Q7 (iii) • Q8 (i) • Q8 (ii) • Q8 (iii) • Q9 •
Question 04 (iii) 

Consider the function iii) Find the xvalues of all the inflection points of f(x). Note: if inflection points do not exist, say so. 
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 

The previous part gave us the derivative of Now, we take the second derivative, set it to zero and look at where the sign changes. 
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Solution  

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Please rate my easiness! It's quick and helps everyone guide their studies. The previous part gave us that Let's compute the second derivative of the function: and then factor it This is plenty enough to get the sign table of the second derivative. And so we see that there are two inflection points, one at x = 1 and one at x = 3. 