AP Calculus AB Mixed Review flashcard 1

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.

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.

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).

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).

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.

Front

What is the limit definition of the first derivative?

Back

f'(x) = lim (h -> 0) [(f(x+h) - f(x)) / h].

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.

Front

How do you find the critical points of a function?

Back

Set the first derivative f'(x) = 0 and solve for x.

Front

What is the second derivative test used for?

Back

To determine the concavity of a function and identify local maxima or minima.

Front

What is the Fundamental Theorem of Calculus?

Back

It states that differentiation and integration are inverse processes.