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Maximization and minimization problems are worked through step-by-step. Maximizing the area enclosed by a given fence length, and minimizing the travel time of a swimmer who has to get to a point on the shore (relates to Snell's law).
Max/Min problem of maximizing area enclosed by a trapezoid inscribed in a semicircle.
Problems and answers without full explanation. Finding tangent lines to an ellipse, minimizing surface area of a grain silo, finding the volume of a solid of revolution, computing an antiderivative using trig substitution, and computing an antiderivative using integration by parts.
Definition of a critical point and its use in finding maxima and minima of a function.
Finding the extremal values of a function, including distinction between local and global maxima and minima.
Iterative divide and conquer method for finding a local maximum or minimum on a curve.
An optimization problem involving two fixed rays and a segment that is allowed to slide between them.
Finding the maximum volume of a box made from two square sheets of metal.
Finding the maximum volume for a trash can made from a cylinder and a hemisphere.
Two problems which involve minimizing the cost of a sculpture and maximizing the area enclosed by a fence.
Fifteen optimization questions drawn from various applications including largest volume of a box, shortest length of fence for a barnyard, and the optimal fare for an airline.
Seven optimization questions which include finding the optimum attack angle for a plane and the best moment to add milk to a cup of coffee to keep it hot.
Two questions which involve minimizing the area of a triangle and minimizing the length of wire needed to brace the legs of a table.
Minimizing the material required to make a popcorn container.
Finding the maximum area of a triangular enclosure formed from two sides of fence and a wall for the third side.