Lesson Worksheet: Rate of Change and Derivatives Mathematics • Higher Education

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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 instantaneous rate of change of at .

Q2:

Evaluate the rate of change of at .

Q3:

Evaluate the instantaneous rate of change of at .

Q4:

Evaluate the rate of change of at .

Q5:

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

Q6:

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

Q7:

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

Q8:

Let with constants , . Determine the constants for which the slope of the tangent to the curve at is .

Q9:

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 .

Q10:

If the function , determine its rate of change when .

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