Unit 3 AP Calculus AB Multiple Choice

Front

What is the Fundamental Theorem of Calculus?

Back

The Fundamental Theorem of Calculus states that if f is a continuous real-valued function on the interval [a, b], and F is an antiderivative of f on [a, b], then: 1) The integral from a to b of f(x)dx = F(b) - F(a). 2) If F is differentiable, then F' = f.

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 difference between a definite and an indefinite integral?

Back

A definite integral computes the accumulation of a quantity over an interval [a, b] and results in a number, while an indefinite integral represents a family of functions and includes a constant of integration (C).

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 Chain Rule in differentiation?

Back

The Chain Rule is a formula for computing the derivative of the composition of two or more functions. If y = f(g(x)), then the derivative is dy/dx = f'(g(x)) * g'(x).

Front

What does it mean for a function to be continuous at a point?

Back

A function f is continuous at a point c if: 1) f(c) is defined, 2) the limit of f(x) as x approaches c exists, and 3) the limit equals f(c).

Front

What is the Power Rule for differentiation?

Back

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

Front

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

Back

Concavity refers to the direction of the curvature of a function's graph. A function is concave up if its second derivative is positive, and concave down if its second derivative is negative.

Front

What is an inflection point?

Back

An inflection point is a point on the graph of a function where the concavity changes, which occurs when the second derivative changes sign.

Front

Explain the concept of optimization in calculus.

Back

Optimization involves finding the maximum or minimum values of a function within a given domain. This often requires finding critical points where the derivative is zero or undefined.