AP Calculus AB 1st Semester Review

Front

What is a point of inflection?

Back

A point on the graph of a function where the concavity changes, indicating a change in the direction of curvature.

Front

How do you find the derivative of y = 2x^-1?

Back

Using the power rule: y' = -2x^-2.

Front

What does it mean for a function to be continuous but not differentiable?

Back

The function has no breaks or holes, but has a sharp corner or cusp at that point.

Front

What is the definition of a limit in calculus?

Back

The value that a function approaches as the input approaches a certain point.

Front

How do you find the limit of a function as x approaches a value?

Back

Substitute the value into the function, if possible, or use limit laws.

Front

What is the power rule for differentiation?

Back

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

Front

What is the difference between a local maximum and a local minimum?

Back

A local maximum is the highest point in a neighborhood, while a local minimum is the lowest point.

Front

What is 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 the chain rule in differentiation?

Back

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

Front

What is the product rule for differentiation?

Back

If y = u*v, then y' = u'v + uv'.