3.1 Calculus Review
Flashcard
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Mathematics
•
12th Grade
•
Practice Problem
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Easy
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Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
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 function at that point.
2.
FLASHCARD QUESTION
Front
What does it mean for a function to be increasing on an interval?
Back
A function f(x) is increasing on an interval if for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).
Tags
CCSS.8.F.B.4
CCSS.HSF.LE.A.2
3.
FLASHCARD QUESTION
Front
How do you find the derivative of a function using the definition?
Back
To find the derivative using the definition, use the formula: f'(x) = lim (h -> 0) [(f(x+h) - f(x))/h].
4.
FLASHCARD QUESTION
Front
What is the Alternate Definition of Derivative?
Back
The Alternate Definition of Derivative states that the derivative of f at a point x is given by f'(x) = lim (h -> 0) [(f(x) - f(x-h))/h].
5.
FLASHCARD QUESTION
Front
What is the slope of a line?
Back
The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.
Tags
CCSS.8.EE.B.5
6.
FLASHCARD QUESTION
Front
What is the relationship between the derivative and the slope of a tangent line?
Back
The derivative of a function at a given point is equal to the slope of the tangent line to the graph of the function at that point.
7.
FLASHCARD QUESTION
Front
What is the significance of the point where the derivative is zero?
Back
A point where the derivative is zero may indicate a local maximum, local minimum, or a point of inflection on the graph of the function.
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