This study assessed the ability of university students enrolled in an introductory calculus course to solve related-rates problems set in geometric contexts.
Students completed a problem-solving test and a test of performance on the individual steps involved in solving such problems.
For an example of this situation, see example #3 below.
5) Using the chain rule, differentiate each side of the equation with respect to time.
Suppose we have a function defined on a closed interval [c, d].
A local maximum or minimum can not occur at the endpoints of this interval because the definition requires that the point is contained in some open interval (a, b).The radius of a sphere is increasing at a rate of 2 meters per second.At what rate is the volume increasing when the radius is equal to 4 meters?3) List all information that is given in the problem and the rate of change that we are trying to find.4) Write an equation that associates the variables with one another.6) Substitute all given information into the equation and solve for the required rate of change.It is important to wait until the equation has been differentiated to substitute information into the equation.Another application of the derivative is in finding how fast something changes.For example, suppose you have a spherical snowball with a 70cm radius and it is melting such that the radius shrinks at a constant rate of 2 cm per minute. These types of problems are called related rates problems because you know a rate and want to find another rate that is related to it.General information is information contained in the problem that is true at all times.Particular information is information that is true only at the particular instant that the problem is asking about.