Using [latex]f(a+h)\approx f(a)+f^{\prime}(a)h[/latex], it is possible to estimate [latex]f(a+h)[/latex] given [latex]f^{\prime}(a)[/latex] and [latex]f(a)[/latex].
The rate of change of position is velocity, and the rate of change of velocity is acceleration. Speed is the absolute value, or magnitude, of velocity.
The population growth rate and the present population can be used to predict the size of a future population.
Marginal cost, marginal revenue, and marginal profit functions can be used to predict, respectively, the cost of producing one more item, the revenue obtained by selling one more item, and the profit obtained by producing and selling one more item.
Glossary
acceleration
is the rate of change of the velocity, that is, the derivative of velocity
amount of change
the amount of a function [latex]f(x)[/latex] over an interval [latex][x,x+h][/latex] is [latex]f(x+h)-f(x)[/latex]
average rate of change
is a function [latex]f(x)[/latex] over an interval [latex][x,x+h][/latex] is [latex]\dfrac{f(x+h)-f(a)}{b-a}[/latex]
marginal cost
is the derivative of the cost function, or the approximate cost of producing one more item
marginal revenue
is the derivative of the revenue function, or the approximate revenue obtained by selling one more item
marginal profit
is the derivative of the profit function, or the approximate profit obtained by producing and selling one more item
population growth rate
is the derivative of the population with respect to time
speed
is the absolute value of velocity, that is, [latex]|v(t)|[/latex] is the speed of an object at time [latex]t[/latex] whose velocity is given by [latex]v(t)[/latex]
