Science:Math Exam Resources/Courses/MATH100/December 2012/Question 06 (d)

MATH100 December 2012

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Question 06 (d)

Full-Solution Problems. In questions 5-11, justify your answers and show all your work. If a box is provided, write your final answer there. Unless otherwise indicated, simplification of numerical answers is required in these questions. 6. Let $f(x)=2x^{3/5}+3x^{-2/5}$. Note that the domain of ƒ is the set of all nonzero real numbers; for example, $f(-1)=-2+3=1$. (d) Find the x-coordinates of all inflection points of $f(x)$.

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
Use the solution to part c and recall that inflection points are points in the domain of the function where the second derivative changes sign.

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Solution
Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. By part c, we see immediately that concavity changes from concave up to concave down at the point $x=7/2$. This is the only inflection point.

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