Unit 2 Flashcard Review: Definition of a derivative

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•
Mathematics
•
9th - 12th Grade
•
Hard
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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 instantaneous rate of change of the function with respect to its variable at that point.
2.
FLASHCARD QUESTION
Front
What does f'(x) represent?
Back
f'(x) represents the derivative of the function f(x), indicating the slope of the tangent line to the graph of f at the point x.
3.
FLASHCARD QUESTION
Front
How do you find the equation of the tangent line to a function at a given point?
Back
The equation of the tangent line can be found using the point-slope form: y - f(a) = f'(a)(x - a), where a is the point of tangency.
4.
FLASHCARD QUESTION
Front
What is the significance of f'(2) = -1 in the context of a function?
Back
It indicates that at x = 2, the slope of the tangent line to the function f(x) is -1, meaning the function is decreasing at that point.
5.
FLASHCARD QUESTION
Front
What does it mean for a function to be differentiable at a point?
Back
A function is differentiable at a point if it has a defined derivative at that point, which implies that the function is continuous and has no sharp corners or vertical tangents there.
6.
FLASHCARD QUESTION
Front
Where is the graph of a function not differentiable?
Back
The graph is not differentiable at points where there are sharp corners, vertical tangents, or discontinuities.
7.
FLASHCARD QUESTION
Front
What is the relationship between the derivative and the slope of a tangent line?
Back
The derivative at a point gives the slope of the tangent line to the graph of the function at that point.
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