# Worksheet: Increasing and Decreasing Intervals of a Function Using Derivatives

In this worksheet, we will practice determining the increasing and decreasing intervals of functions using the first derivative of a function.

**Q1: **

Find all possible intervals on which the function is increasing and 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 .

**Q2: **

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 .

**Q4: **

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 increases up to a certain point and then decreases.
- BThe concentration of the drug increases.
- CThe concentration of the drug does not change.

**Q5: **

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 .

**Q6: **

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 .

**Q7: **

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: **

Find the intervals on which the function is increasing and decreasing.

- AThe function is increasing on .
- BThe function is increasing on .
- CThe function is decreasing on .
- DThe function is decreasing on .
- EThe function is decreasing on .

**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: **

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 .

**Q11: **

Determine the intervals on which the function is increasing and decreasing.

- AThe function is decreasing on and increasing on and .
- BThe function is decreasing on and increasing on and .
- CThe function is decreasing on and and increasing on .
- DThe function is decreasing on and increasing on and .
- EThe function is decreasing on and and increasing on .

**Q12: **

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 .

**Q13: **

Determine the intervals on which the function is increasing and decreasing.

- Aincreasing over
- Bdecreasing over
- Cincreasing over
- Dincreasing over
- Eincreasing over , decreasing over

**Q14: **

Determine the intervals over which the function is increasing and over which it is decreasing.

- Adecreasing over
- Bdecreasing over the interval , increasing over the interval
- Cincreasing over
- D decreasing over the interval , increasing over the interval
- Edecreasing over the interval , increasing over the interval

**Q15: **

Let Find the intervals on which is increasing and where it is decreasing.

- Aincreasing over the interval , decreasing over the interval
- Bdecreasing over
- Cincreasing over the interval , decreasing over the interval
- Ddecreasing over the interval , increasing over the interval
- Eincreasing over

**Q16: **

Determine the intervals on which the function is increasing and where it is decreasing.

- Aincreasing over
- Bincreasing over the intervals and , decreasing over the interval
- Cdecreasing over
- Dincreasing over the interval , decreasing over the intervals and

**Q17: **

Determine the intervals over which the function is increasing and over which it is decreasing.

- Aincreasing over the interval , decreasing over the intervals and
- Bincreasing over the interval
- Cincreasing over
- Dincreasing over
- Edecreasing over the interval , increasing over the intervals and

**Q18: **

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 .

**Q19: **

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 and decreasing on .
- CThe function is increasing on and decreasing on and .
- DThe function is increasing on and decreasing on and .
- EThe function is increasing on and decreasing on and .

**Q21: **

Determine the intervals on which the function , where , is increasing and where it is 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 .
- EThe function is decreasing on .

**Q22: **

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 .

**Q23: **

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

**Q24: **

Determine the intervals on which the function is increasing and where it is decreasing.

- Aincreasing over
- Bdecreasing over
- Cdecreasing on the interval , increasing on the interval
- Ddecreasing over

**Q25: **

Determine the intervals on which the function is increasing and on which it is decreasing.

- Adecreasing on
- Bdecreasing on
- Cdecreasing on , increasing on
- Dincreasing on
- Edecreasing on , increasing on