Calc AB EOY Final

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 in a function.

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 the Chain Rule in differentiation?

Back

The Chain Rule states that if a function y = f(g(x)) is composed of two functions, then the derivative is dy/dx = f'(g(x)) * g'(x).

Front

What is an inflection point?

Back

An inflection point is a point on the curve of a function where the concavity changes, which can be found by analyzing the second derivative.

Front

Define a critical point in calculus.

Back

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

Front

What is 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

Explain the concept of Riemann sums.

Back

Riemann sums are a method for approximating the total area under a curve by dividing it into rectangles and summing their areas.

Front

What is the difference between definite and indefinite integrals?

Back

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