Science:Math Exam Resources/Courses/MATH100 A/December 2023/Question 13

MATH100 A December 2023

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Question 13
Graph of a function Consider the following graph of a derivative $f'$. Find all the intervals where $f$ is concave down.

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
By definition, a function is concave down at $x$ if its derivative at $x$ is decreasing.

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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. The graph pictured is decreasing for $x\in (-3,0)$, so, since the graph is of the derivative $f'$, the function $f$ is concave down on the interval $(-3,0)$.