Unit 1 Calculus AB Multiple Choice

Front

What is the definition of a derivative?

Back

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero. It represents the slope of the tangent line to the graph of the function at that point.

Front

What is the Power Rule for differentiation?

Back

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

Front

Explain the concept of limits in calculus.

Back

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

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 f'(g(x)) * g'(x).

Front

Define the term 'critical point' in calculus.

Back

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

Front

What is the Mean Value Theorem?

Back

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

Front

What does it mean for a function to be continuous 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 the difference between a local maximum and a global maximum?

Back

A local maximum is the highest point in a specific neighborhood of the function, while a global maximum is the highest point over the entire domain of the function.

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 determined by the second derivative.

Front

Explain the concept of concavity.

Back

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