Given the position function of a particle, you can calculate all kinds of information about the particle, including its velocity and acceleration.

A position function describes the position of an object over time.

L’Hospital’s rule is used to get you out of sticky situations with indeterminate limit forms. If you plug into the function the number you’re approaching and your result is indeterminate, you should apply L’Hospital’s rule. To use it, take the derivatives of the numerator and denominator and replace the original numerator and denominator with their derivatives. Then plug in the number you’re approaching. If you still get an indeterminate form, continue using L’Hospital’s rule until you can use substitution to get a prettier answer (one that's not an indeterminate form).

Newton's method is a way to approximate the root of a function (the point at which it crosses the x-axis), without having to solve for it exactly.

The Mean Value Theorem guarantees that, at some point inside of a closed interval, the tangent line to the graph will be parallel to the line connecting the endpoints of that interval.

Find the rate of change of the top of a ladder when the ladder is sliding down and away from the wall at a specified rate.

Find the rate of change of the distance between an observer and an airplane when the airplane is traveling at a specified rate.

Find the rate of change of the water level in a water tank when the volume of water changes at a specified rate.

Find the rate of change of the price of an item when the quantity supplied changes at a specified rate.