AP Calculus AB 1st Semester Review

Front

Back

Front

Identify where the graph of a function is not differentiable: x = -2, -1, 1.

Back

The graph is not differentiable at x = -2, -1, 1.

Front

What is the best way to justify finding the absolute maximum of a function?

Back

A table including end points and critical points, and the values you get when you plug into the function.

Front

Back

Front

Back

The average rate of change is 1.

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.

Front

What is a critical point?

Back

A critical point occurs where the derivative is zero or undefined.

Front

Explain the Mean Value Theorem.

Back

The Mean Value Theorem states that if a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one point c in the interval where the derivative equals the average rate of change.

Front

What is the relationship between the first derivative and the increasing/decreasing behavior of a function?

Back

If the first derivative is positive, the function is increasing; if negative, the function is decreasing.

Front

Define the second derivative test for local extrema.

Back

The second derivative test states that if f''(c) > 0, then f has a local minimum at c; if f''(c) < 0, then f has a local maximum at c.