AP Calculus AB 1st Semester Review

Front

Where is the graph not differentiable?

Back

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

Front

If the radius of a circle is changing at a rate of 5 in/sec, how fast is the area of the outer circle changing when the diameter is 8 in?

Back

The area of the outer circle is changing at a rate of 40π in/sec.

Front

If A = 2x^3, what is (dA/dt)?

Back

(dA/dt) = 6x^2 (dx/dt).

Front

If H(x) = f^-1(x), what is H'(3)?

Back

H'(3) = 1/4.

Front

What theorem states that if you have a closed, continuous interval, there MUST be an absolute max and min?

Back

Extreme Value Theorem.

Front

Define differentiability in calculus.

Back

A function is differentiable at a point if it has a defined derivative at that point.

Front

What is the relationship between a function and its derivative?

Back

The derivative of a function represents the rate of change of the function with respect to its variable.

Front

State 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 formula for the area of a circle?

Back

A = πr^2, where r is the radius.

Front

Explain the concept of related rates in calculus.

Back

Related rates involve finding the rate at which one quantity changes in relation to another quantity.