AP Calculus AB Mixed Review flashcard 1

Front

What is the definition of continuity at a point?

Back

A function f(x) is continuous at a point x = a if the following three conditions are met: 1) f(a) is defined, 2) the limit of f(x) as x approaches a exists, and 3) the limit equals f(a).

Front

How do you find the derivative of an inverse function?

Back

If g is the inverse of f, then g'(y) = 1 / f'(g(y)).

Front

What is the limit definition of the first derivative?

Back

The first derivative of a function f at a point x is defined as f'(x) = lim (h -> 0) [(f(x+h) - f(x)) / h].

Front

How do you calculate the average rate of change of a function over an interval?

Back

The average rate of change of a function f from x = a to x = b is given by (f(b) - f(a)) / (b - a).

Front

What is the equation of a tangent line at a point on a curve?

Back

The equation of the tangent line to the curve y = f(x) at the point (a, f(a)) is given by y - f(a) = f'(a)(x - a).

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = n*x^(n-1).

Front

What is the product rule for differentiation?

Back

If u(x) and v(x) are functions, then the derivative of their product is (uv)' = u'v + uv'.

Front

What is the quotient rule for differentiation?

Back

If u(x) and v(x) are functions, then the derivative of their quotient is (u/v)' = (u'v - uv') / v^2.

Front

What is the chain rule for differentiation?

Back

If y = f(g(x)), then the derivative is dy/dx = f'(g(x)) * g'(x).

Front

What is the significance of the second derivative?

Back

The second derivative, f''(x), indicates the concavity of the function: if f''(x) > 0, the function is concave up; if f''(x) < 0, it is concave down.