Science:Math Exam Resources/Courses/MATH110/April 2017/Question 06 (b)
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Question 06 (b) |
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Consider a function that is continuous and differentiable everywhere except at and , and such that it satisfies ALL of the following conditions:
(b) List the -coordinates of all inflection points of , if they exist. Explain why they are inflection points. |
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 |
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The function f has an inflection point at x if f is differentiable at x and if the sign of changes at x. Take a look at the places where the sign of changes and exclude the points x=-2 and x=2, because f(x) is not differentiable at those points. |
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Solution |
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Please rate my easiness! It's quick and helps everyone guide their studies. The inflection points of f occur at the x-values where is differentiable, but where changes sign. To this end, we notice that changes sign at -5, -2, 0, 2, and 5, but is not differentiable at -2 or 2. So the only inflection points of f occur at -5 and 5. Answer: |