Application of Derivatives.

12 lessons96 min3 simulations

The derivative measures how fast one quantity changes against another, and this chapter puts that to work. It turns rates into answers for growing circles, filling tanks and moving shadows, reads marginal cost and revenue in economics, uses the sign of f′ to tell where a function rises or falls, and locates the highest and lowest points of a graph with the first and second derivative tests. It ends with optimisation: setting up one quantity to be made largest or smallest, and checking every candidate on a closed interval.

Also called: maxima and minima · tangents and normals · increasing and decreasing functions