Science:Math Exam Resources/Courses/MATH100 A/December 2023/Question 03
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Question 03 |
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A function is pictured. Sketch the graph of the derivative directly on the axes. |
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 graph of the function consists of the points , where is the slope of the line that is tangent to at the value . It is useful to start with the points where the slope is 0. |
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
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Solution |
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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 of is pictured in red, on top of the graph of . The essential aspect is that the derivative is 0 (or intersects the -axis) at every for which the original function attains a local minimum or maximum, and the derivative is positive or negative (is above or below the -axis) at every for which the original function is increasing or decreasing, respectively. |