AP Calculus AB - Derivatives and Antiderivatives Review

Flashcards covering vocabulary terms related to derivatives, antiderivatives, and fundamental calculus concepts.

Derivative

A measure of how a function changes as its input changes, represents the rate of change of a function.

Chain Rule

A formula to compute the derivative of a composite function.

Average Rate of Change

The change in the value of a function divided by the change in the input over an interval.

Product Rule

A formula for finding the derivative of the product of two functions, stating that (uv)' = u'v + uv'.

Mean Value Theorem

A theorem that states that if a function is continuous and differentiable over an interval, there exists a point where the instantaneous rate of change equals the average rate of change.

Quotient Rule

A formula for finding the derivative of a quotient of two functions, given by (u/v)' = (u'v - uv')/v².

Limit Definition of Derivative

The derivative of a function at a point is defined as the limit of the average rate of change as the interval approaches zero.

Antiderivative

A function whose derivative is the original function, essentially the reverse operation of differentiation.

Fundamental Theorem of Calculus

A theorem that links the concept of differentiation and integration, establishing a relationship between the two.

Average Value of a Function

The average height of the graph of a function over a given interval, calculated as (1/(b-a)) ∫[a,b] f(x) dx.