AP Calculus AB

Front

What is the Fundamental Theorem of Calculus?

Back

The Fundamental Theorem of Calculus links the concept of differentiation and integration, stating that if F is an antiderivative of f on an interval [a, b], then ∫_a^b f(x) dx = F(b) - F(a).

Front

Define a derivative in the context of calculus.

Back

A derivative represents the rate of change of a function with respect to a variable. It is defined as the limit of the average rate of change of the function as the interval approaches zero.

Front

What is the definition of an indefinite integral?

Back

An indefinite integral, or antiderivative, of a function f(x) is a function F(x) such that F'(x) = f(x). It is represented as ∫f(x)dx + C, where C is the constant of integration.

Front

Explain the concept of limits in calculus.

Back

A limit is a fundamental concept in calculus that describes the behavior of a function as its argument approaches a particular point. It is used to define continuity, derivatives, and integrals.

Front

What is the difference between a definite and an indefinite integral?

Back

A definite integral computes the net area under a curve between two specified limits and results in a numerical value, while an indefinite integral represents a family of functions and includes a constant of integration.

Front

What is the power rule for differentiation?

Back

The power rule states that if f(x) = x^n, then the derivative f'(x) = n*x^(n-1), where n is a real number.

Front

What is the product rule for differentiation?

Back

The product rule states that if u(x) and v(x) are two differentiable functions, then the derivative of their product is given by (uv)' = u'v + uv'.

Front

What is the quotient rule for differentiation?

Back

The quotient rule states that if u(x) and v(x) are two differentiable functions, then the derivative of their quotient is given by (u/v)' = (u'v - uv')/v^2.

Front

What is a critical point in calculus?

Back

A critical point of a function occurs where its derivative is zero or undefined. Critical points are used to find local maxima and minima.

Front

Define concavity in the context of a function's graph.

Back

Concavity refers to the direction in which a function curves. A function is concave up if its second derivative is positive and concave down if its second derivative is negative.