Practice Increasing And Decreasing Functions (3)

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8 questions

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6 sample questions

Question 1.
Define what it means for a function to be increasing.
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Think about the movement of the graph as you move from left to right.
Question 2.
How can you determine if a function is decreasing using derivatives?
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Remember the sign of the derivative!
3Question 3.
What indicates that a function is increasing on an interval?
- f′(x) < 0
- f′(x) = 0
- f′(x) > 0
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Consider the definition.
4Question 4.
True or False: If a function is decreasing, then f′(x) > 0 for all x in that interval.
- True
- False
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Think of the graph slope.
Question 5.
For f(x) = 2x³ - 4x² + 1, find intervals of increase and decrease and justify your answer.
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Examine the signs of the derivative!
Question 6.
Show that the function f(x) = -x³ + 3x² - 2 has a local maximum at a specific point.
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Look for sign changes in the first derivative.

4 more questions in this section. Enroll free to practise them all.