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Lesson Worksheet: Increasing and Decreasing Intervals of a Function Using Derivatives Mathematics • Higher Education
In this worksheet, we will practice determining the increasing and decreasing intervals of functions using the first derivative of a function.
Q2:
Determine the intervals on which is increasing or decreasing.
- AThe function is decreasing on and and increasing on and .
- BThe function is decreasing on and and increasing on and .
- CThe function is decreasing on and and increasing on and .
- DThe function is decreasing on and and increasing on and .
- EThe function is decreasing on and and increasing on and .
Q3:
For , find the intervals on which is increasing or decreasing.
- AThe function is decreasing on and increasing on .
- BThe function is decreasing on and increasing on .
- CThe function is decreasing on and increasing on .
- DThe function is decreasing on and increasing on .
- EThe function is decreasing on and increasing on .
Q4:
Given that , , determine the intervals on which is increasing or decreasing.
- A is increasing on the intervals and and decreasing on the interval .
- B is increasing on the interval and decreasing on the intervals and .
- C is increasing on the interval and decreasing on the intervals and .
- D is decreasing on the interval and decreasing on the interval .
- E is increasing on the intervals and and decreasing on the interval .
Q6:
Given that , find the intervals on which is increasing or decreasing.
- A is decreasing on the interval and decreasing on the interval .
- B is increasing on the interval and decreasing on the interval .
- C is increasing on the interval and decreasing on the interval .
- D is increasing on the interval and decreasing on the interval .
- E is increasing on the interval and decreasing on the interval .
Q8:
Determine the intervals on which the function is increasing and where it is decreasing.
- Aincreasing on the intervals and , decreasing on the interval
- Bincreasing on the interval , decreasing on the interval
- Cdecreasing on the intervals and , increasing on the interval
- Ddecreasing on the interval , increasing on the interval
Q9:
Find the intervals on which the function is increasing and decreasing.
- AThe function is increasing on and decreasing on .
- BThe function is increasing on and decreasing on .
- CThe function is increasing on and decreasing on .
- DThe function is increasing on and decreasing on .
- EThe function is increasing on and decreasing on .
Q10:
Let . Determine the intervals where this function is increasing and where it is decreasing.
- A is increasing on the intervals and and decreasing on the interval .
- B is increasing on the intervals and and decreasing on the interval .
- C is decreasing on the interval and decreasing on the intervals and .
- D is increasing on the interval and decreasing on the intervals and .
- E is increasing on the interval and decreasing on the intervals and .