AP Calculus Unit 6A Multiple Choice Qs

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).

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

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.

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.

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

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).

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.

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.

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.

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.