AP Calculus AB Mixed Review flashcard 1

Flashcard
•
Mathematics
•
11th - 12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the definition of an inverse function?
Back
An inverse function reverses the operation of the original function. If f(x) = y, then the inverse function g(y) = x.
2.
FLASHCARD QUESTION
Front
How do you find the derivative of an inverse function at a point?
Back
Use the formula g'(y) = 1 / f'(g(y)), where g is the inverse of f.
3.
FLASHCARD QUESTION
Front
What is the formula for the derivative of a polynomial function?
Back
For f(x) = ax^n, the derivative f'(x) = n * ax^(n-1).
4.
FLASHCARD QUESTION
Front
What is the equation of a tangent line at a point (x_0, f(x_0))?
Back
The equation is y - f(x_0) = f'(x_0)(x - x_0).
5.
FLASHCARD QUESTION
Front
What does the limit of a function represent?
Back
The limit represents the value that a function approaches as the input approaches a certain point.
6.
FLASHCARD QUESTION
Front
What is the limit definition of the first derivative?
Back
f'(x) = lim (h -> 0) [(f(x+h) - f(x)) / h].
7.
FLASHCARD QUESTION
Front
What is the relationship between position, velocity, and acceleration?
Back
Velocity is the first derivative of position, and acceleration is the first derivative of velocity.
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