Practice finding the linear approximation to a function and using it to estimate the value of the function at a nearby point.
When two variables are related by an equation their derivatives are also related.
Find the rate at which the radius of a balloon is increasing as it is blown up.
Find the rate at which the depth of water increases as water is poured into a cone.
Find the rate atwhich a ladder slides down a wall as the base is pulled away from the wall.
Find the rate at which the distance between two objects if changing.
Find the rate at which the angle of sight to a tightrope walker changes as she walks along a wire.
Find the rate at which the distance to an airplane is increasing as the airplane ascends.
Given the position of an object, find its velocity and acceleration.
Practice using l'Hospital's rule for computing limits.
Find the parametric formula for the line tangent to a parametric curve.
Practice identifying the graphs of the first and second derivatives of a function given the formula and/or the plot of the function.
Learn the terminology to describe the properties of the graph of a function.
Learn to identify the properties of a function, its derivative, and its second derivative from the graph of the function.
Learn to identify the properties of a function, its derivative, and its second derivative from the graph of the first derivative.
Learn to identify the properties of a function, its derivative, and its second derivative from the graph of the second derivative.
Find the shape of a function near a vertical aymptote or vertical tangent.
Find the critical points of a function and classify them using the Second Derivative Test.
Minimize the surface area of a tin can with fixed volume.
Maximize the area of a field enclosed in a fence with several pens.
Minimize the surface area of a box with a square base and fixed volume.
Maximize the area of a rectangle inscribed in an ellipse or part of an ellipse.
Minimize the distance from a point to a line.
Minimize the time needed to row across a river and run downstream.
Practice finding the linear and quadratic approximations to a function and using them to estimate the value of the function at a nearby point.
Version 1.3.1
Supported in part by NSF DUE CCLI Grants 0737209 (Meade) and 0737248 (Yasskin)