What is the definition of a derivative?
Unit 1 Calculus AB Multiple Choice

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Mathematics
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12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
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.
2.
FLASHCARD QUESTION
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.
3.
FLASHCARD QUESTION
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.
4.
FLASHCARD QUESTION
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).
5.
FLASHCARD QUESTION
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.
6.
FLASHCARD QUESTION
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).
7.
FLASHCARD QUESTION
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.
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