# Worksheet: Rate of Change and Derivatives

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

Q1:

Evaluate the rate of change of at .

Q2:

Evaluate the rate of change of at .

Q3:

Find the rate of change of with respect to when .

Q4:

Evaluate the rate of change of at .

• A4
• B
• C
• D

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
• B
• C9
• D
• E

Q9:

Evaluate the rate of change of at .

• A3
• B
• C
• D
• E5

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 disk 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:

What is the rate of change for the function ?

Q15:

Evaluate the rate of change of at .

• A
• B
• C
• D

Q16:

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 ?

Q17:

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,

Q18:

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

Q19:

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

Q20:

Find the rate of change of when .

Q21:

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

Q22:

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

Q23:

A population’s size after days is given by . Find the rate of change in the population when .

Q24:

Evaluate the rate of change of at .

• A
• B
• C

Q25:

Find the slope of the tangent to the curve at .

• A180
• B225
• C45
• D90