In this worksheet, we will practice finding the instantaneous rate of change for a function using derivatives and applying this in real-world problems.

**Q5: **

If the function , determine its rate of change when .

- A
- B
- C
- D
- E

**Q6: **

What is the rate of change for the function ?

**Q7: **

Determine the rate of change of the function at .

- A
- B
- C
- D

**Q8: **

Evaluate the rate of change of at .

- A
- B9
- C
- D
- E

**Q9: **

Evaluate the rate of change of at .

- A3
- B
- C5
- D
- E

**Q10: **

Evaluate the rate of change of at .

- A
- B
- C
- D

**Q11: **

Find the rate of change of when and determine, to the nearest minute, the positive angle between the tangent at and the positive -axis.

- A ,
- B ,
- C ,
- D ,

**Q12: **

A circular disc preserves its shape as it shrinks. What is the rate of change of its area with respect to radius when the radius is 59 cm?

- A
cm
^{2}/cm - B
cm
^{2}/cm - C
cm
^{2}/cm - D
cm
^{2}/cm

**Q13: **

A length is initially 9 cm and increases at a rate of 3 cm/s. Write the length as a function of time, .

- A
- B
- C
- D

**Q14: **

Determine the rate of change of the function when .

- A
- B
- C
- D

**Q15: **

What is the rate of change for the function ?

**Q16: **

If the function , find the rate-of-change function when .

- A
- B
- C
- D
- E

**Q17: **

Evaluate the rate of change of at .

- A
- B
- C
- D

**Q18: **

The biomass of a bacterial culture in milligrams as a function of time in minutes is given by . What is the rate of growth of the culture when ?

**Q19: **

Let . Suppose that the change in as goes from to 2 is 6 and that the rate of change of at is 17. Determine and .

- A ,
- B ,
- C ,
- D ,

**Q20: **

A particle moves along the curve . At what point is the rate of change in its -coordinate four times the rate of change of its -coordinate?

- A
- B
- C
- D

**Q21: **

Find the rate of change of the slope of the tangent of function at .

**Q22: **

Find the rate of change of when .

**Q23: **

The output in mg of a chemical reaction after seconds is given by . What is the rate of production of this reaction at seconds?

**Q24: **

The distance in metres travelled by a body in seconds is . What is the rate of change of with respect to when ?