ROC, Tangent Lines, and Derivative

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
+1
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1.
FLASHCARD QUESTION
Front
What is the first derivative of a function?
Back
The first derivative of a function, denoted as f'(x), y', or dy/dx, represents the rate of change of the function with respect to its variable.
Tags
CCSS.HSF.LE.B.5
2.
FLASHCARD QUESTION
Front
What does the limit definition of the first derivative state?
Back
The limit definition of the first derivative states that f'(x) = lim (h -> 0) [(f(x+h) - f(x))/h], which describes the slope of the tangent line to the curve at a point.
3.
FLASHCARD QUESTION
Front
How do you find the equation of a tangent line to a function at a given point?
Back
To find the equation of a tangent line, calculate the derivative at the point to find the slope, then use the point-slope form of a line: y - f(a) = f'(a)(x - a).
4.
FLASHCARD QUESTION
Front
What is the average rate of change of a function?
Back
The average rate of change of a function between two points is calculated as (f(b) - f(a)) / (b - a), representing the slope of the secant line connecting the two points.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
5.
FLASHCARD QUESTION
Front
If a function's derivative is negative, what does this indicate about the function?
Back
If a function's derivative is negative, it indicates that the function is decreasing in that interval.
Tags
CCSS.HSF.IF.B.4
6.
FLASHCARD QUESTION
Front
What is the significance of a positive first derivative?
Back
A positive first derivative indicates that the function is increasing in that interval.
7.
FLASHCARD QUESTION
Front
What does the second derivative tell us about a function?
Back
The second derivative indicates the concavity of the function: if it is positive, the function is concave up; if negative, concave down.
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