MATH100 December 2015
• Q1 (i) • Q1 (ii) • Q1 (iii) • Q1 (iv) • Q2 (i) • Q2 (ii) • Q2 (iii) • Q2 (iv) • Q3 (i) • Q3 (ii) • Q3 (iii) • Q3 (iv) • Q4 (a) • Q4 (b) • Q4 (c) • Q4 (d) • Q5 (a) • Q5 (b) • Q5 (c) • Q5 (d) • Q6 (a) • Q6 (b) • Q6 (c) • Q6 (d) • Q7 • Q8 (a) • Q8 (b) • Q9 • Q10 (a) • Q10 (b) • Q10 (c) • Q10 (d) • Q10 (e) • Q10 (f) • Q10 (g) • Q10 (h) • Q11 (a) • Q11 (b) • Q12 (a) • Q12 (b) • Q12 (c) •
Question 05 (c)
Find the coordinates of the inflection point of the function .
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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What's the definition of the inflection point?
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Recall the is an inflection point if and only if and changes its sign at .
Differentiating using the product rule, we obtain and
using the product rule again, .
Since for all , if and only if .
Also, we observe that changes sign at . More precisely,
for and for .
This implies that is the inflection point.
Therefore, the answer is .