AB Calculus Semester 1 review

Front

The acceleration function is the first derivative of...

Back

velocity

Front

Compute the limit as x approaches 0 of (sin x)/x.

Back

1

Front

The image displays the ______

Back

Limit definition of the first derivative

Front

The function shown is the graph of f '(x), the derivative of f(x). The domain is [-3,5]. On which interval is the graph of f(x) concave upward?

Back

(-1,1) & (3,5]

Front

What does this picture represent?

Back

Right Riemann Sum

Front

What is the Fundamental Theorem of Calculus?

Back

It links the concept of differentiation and integration, stating that if F is an antiderivative of f on an interval [a, b], then ∫_a^b f(x)dx = F(b) - F(a).

Front

Define the Mean Value Theorem.

Back

If a function is continuous on [a, b] and differentiable on (a, b), then there exists at least one c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).

Front

What is a critical point?

Back

A point on the graph of a function where the derivative is zero or undefined.

Front

What does the Squeeze Theorem state?

Back

If f(x) ≤ g(x) ≤ h(x) for all x in some interval and lim x→c f(x) = lim x→c h(x) = L, then lim x→c g(x) = L.

Front

What is the definition of a derivative?

Back

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero.