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 cm2/cm
- B cm2/cm
- C cm2/cm
- D cm2/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 ?