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Worksheet: Increasing and Decreasing Intervals of a Function Using Derivatives
Q1:
Find the intervals on which the function is either increasing or decreasing.
- AThe function is increasing on .
- BThe function is decreasing on and .
- CThe function is decreasing on .
- DThe function is increasing on and .
- EThe function is increasing on and .
Q2:
Find all possible intervals on which the function is increasing and decreasing.
- A The function is decreasing on , and increasing on .
- B The function is decreasing on , and increasing on .
- C The function is decreasing on , and increasing on .
- D The function is decreasing on , and increasing on .
- E The function is decreasing on , and increasing on .
Q3:
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 .
Q4:
Determine the intervals on which the function is increasing and on which it is decreasing.
- Aincreasing on the interval
- Bincreasing on the interval, decreasing on the interval
- Cdecreasing on the interval
- Ddecreasing on the interval, increasing on the interval
Q5:
Find the intervals on which the function is increasing and decreasing.
- A The function is increasing on and decreasing on .
- B The function is increasing on and decreasing on .
- C The function is increasing on and decreasing on .
- D The function is increasing on and decreasing on .
- E The function is increasing on and decreasing on .
Q6:
Determine the intervals on which the function is increasing and decreasing.
- AThe function is decreasing on and and increasing on .
- BThe function is decreasing on and increasing on and .
- CThe function is decreasing on and increasing on and .
- D The function is decreasing on and and increasing on .
- EThe function is decreasing on and increasing on and .
Q7:
Determine the intervals on which the function , where , is increasing and where it is decreasing.
- A The function is increasing on and decreasing on .
- B The function is decreasing on .
- CThe function is increasing on and decreasing on .
- D The function is increasing on .
- E The function is increasing on and decreasing on .
Q8:
Given that , find the intervals on which is increasing or decreasing.
- A is increasing 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 decreasing on the interval and decreasing on the interval .
Q9:
For , find the intervals on which is increasing or decreasing.
- A The function is decreasing on and increasing on .
- B The function is decreasing on and increasing on .
- C The function is decreasing on and increasing on .
- D The function is decreasing on and increasing on .
- E The function is decreasing on and increasing on .
Q10:
Let Find the intervals on which is increasing and where it is decreasing.
- Aincreasing over the interval , decreasing over the interval
- Bincreasing over the interval , decreasing over the interval
- Cincreasing over
- Ddecreasing over the interval , increasing over the interval
- Edecreasing over
Q11:
Determine the intervals on which the function is increasing and where it is decreasing.
- Aincreasing on the interval , decreasing on the interval
- Bincreasing on the intervals and , decreasing on the interval
- Cdecreasing on the interval , increasing on the interval
- Ddecreasing on the intervals and , increasing on the interval
Q12:
Find the intervals on which the function is increasing and decreasing.
- A The function is decreasing on .
- BThe function is increasing on .
- CThe function is increasing on .
- D The function is decreasing on .
- E The function is decreasing on .
Q13:
Determine the intervals on which the function is increasing and where it is decreasing.
- A increasing over
- B increasing over the interval , decreasing over the intervals and
- C decreasing over
- D increasing over the intervals and , decreasing over the interval
Q14:
Determine the intervals over which the function is increasing and over which it is decreasing.
- Aincreasing over
- Bincreasing over the interval
- Cincreasing over
- Ddecreasing over the interval , increasing over the intervals and
- Eincreasing over the interval , decreasing over the intervals and
Q15:
Given that , determine the intervals on which is increasing or decreasing.
- A is increasing on the intervals and and decreasing on the intervals and .
- B is increasing on the intervals and and decreasing on the intervals and .
- C is increasing on the intervals and and decreasing on the intervals and .
- D is increasing on the intervals and and decreasing on the intervals and .
- E is increasing on the intervals and and decreasing on the intervals and .
Q16:
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 increasing on the intervals and and decreasing on the interval .
- E is decreasing on the interval and decreasing on the interval .
Q17:
Determine the intervals on which the function is increasing or decreasing.
- AThe function is increasing on and and decreasing on .
- BThe function is increasing on and decreasing on and .
- CThe function is increasing on and decreasing on and .
- DThe function is increasing on and and decreasing on .
- EThe function is increasing on and decreasing on and .
Q18:
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 increasing on the interval and decreasing on the intervals and .
- D is increasing on the interval and decreasing on the intervals and .
- E is decreasing on the interval and decreasing on the intervals and .
Q19:
The concentration of a drug in a patientβs bloodstream hours after injection is given by . How does the concentration change as increases?
- AThe concentration of the drug does not change.
- BThe concentration of the drug increases.
- CThe concentration of the drug increases up to a certain point and then decreases.
Q21:
Determine the intervals on which the function is increasing and where it is decreasing.
- Adecreasing on the interval , increasing on the interval
- Bdecreasing over
- Cdecreasing over
- Dincreasing over
Q22:
Determine the intervals on which the function is increasing and on which it is decreasing.
- A decreasing on , increasing on
- B decreasing on , increasing on
- C decreasing on
- D decreasing on
- E increasing on
Q23:
Determine the intervals on which the function is increasing and decreasing.
- Aincreasing over
- Bincreasing over
- Cdecreasing over
- Dincreasing over
- Eincreasing over , decreasing over
Q24:
Determine the intervals over which the function is increasing and over which it is decreasing.
- Aincreasing over
- Bdecreasing over the interval , increasing over the interval
- Cdecreasing over
- D decreasing over the interval , increasing over the interval
- Edecreasing over the interval , increasing over the interval
Q25:
Determine the intervals on which is increasing or decreasing.
- A The function is decreasing on and and increasing on and .
- B The function is decreasing on and and increasing on and .
- C The function is decreasing on and and increasing on and .
- D The function is decreasing on and and increasing on and .
- E The function is decreasing on and and increasing on and .