# Worksheet: The Rate of Change as a Derivative

Q1:

Determine the rate of change of the function when .

• A
• B
• C
• D

Q2:

What is the rate of change for the function ?

Q3:

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

• A
• B
• C
• D
• E

Q4:

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

• A
• B
• C
• D
• E

Q5:

Evaluate the rate of change of at .

• A
• B
• C
• D

Q6:

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 ?

Q7:

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 ?

Q8:

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 ,

Q9:

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

Q10:

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

• A
• B
• C
• D

Q11:

Find the rate of change of when .

Q12:

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

Q13:

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

• A248
• B238
• C 1β015
• D203

Q14:

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

• A237
• B225
• C648
• D216