AP Calculus Unit 6A Multiple Choice Qs

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 limit in calculus.

Back

A limit is a value that a function approaches as the input approaches some value. It is fundamental in defining derivatives and integrals.

Front

What is the derivative of a function?

Back

The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point, representing the rate of change of the function.

Front

Explain the concept of continuity at a point.

Back

A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point.

Front

What is a critical point in calculus?

Back

A critical point of a function is where its derivative is zero or undefined, indicating potential local maxima or minima.

Front

Define the Mean Value Theorem.

Back

The Mean Value Theorem states that if a function is continuous on [a, b] and differentiable on (a, b), then there exists at least one c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).

Front

What is the difference between definite and indefinite integrals?

Back

A definite integral computes the area under a curve between two points and results in a number, while an indefinite integral represents a family of functions and includes a constant of integration.

Front

What is L'Hôpital's Rule?

Back

L'Hôpital's Rule is a method for finding limits of indeterminate forms (0/0 or ∞/∞) by taking the derivative of the numerator and denominator.

Front

Explain the concept of concavity.

Back

Concavity refers to the direction of the curvature of a 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 can be found where the second derivative is zero or undefined.