Unit 3 Calculus Test
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the definition of a derivative in calculus?
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 function's graph at that point.
2.
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.
3.
FLASHCARD QUESTION
Front
What is the power rule for differentiation?
Back
The power rule states that if f(x) = x^n, then the derivative f'(x) = n*x^(n-1).
4.
FLASHCARD QUESTION
Front
Define the term 'critical point' in the context of 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.
5.
FLASHCARD QUESTION
Front
What is the difference between a local maximum and a local minimum?
Back
A local maximum is a point where the function value is higher than all nearby points, while a local minimum is a point where the function value is lower than all nearby points.
6.
FLASHCARD QUESTION
Front
State 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).
7.
FLASHCARD QUESTION
Front
What is the chain rule in differentiation?
Back
The chain rule is a formula for computing the derivative of the composition of two or more functions. If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).
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