AP Calc AB Review for QZ 17-18

Front

What is the Mean Value Theorem?

Back

The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).

Front

What are the conditions required for the Mean Value Theorem to apply?

Back

The function must be continuous on the closed interval [a, b] and differentiable on the open interval (a, b).

Front

What does it mean for a function to be continuous on a closed interval?

Back

A function is continuous on a closed interval [a, b] if it does not have any breaks, jumps, or asymptotes in that interval.

Front

What does it mean for a function to be differentiable on an open interval?

Back

A function is differentiable on an open interval (a, b) if it has a derivative at every point in that interval.

Tags

CCSS.HSF-LE.A.1B

Front

What is the relationship between velocity and acceleration?

Back

Acceleration is the derivative of velocity with respect to time.

Front

How can you determine if a particle's speed is decreasing?

Back

A particle's speed is decreasing if its velocity and acceleration have different signs.

Front

What is the significance of the number c in the Mean Value Theorem?

Back

The number c represents a point in the interval (a, b) where the instantaneous rate of change (slope of the tangent) equals the average rate of change (slope of the secant line) over the interval.

Front

What is the formula for the Mean Value Theorem?

Back

f'(c) = (f(b) - f(a)) / (b - a) for some c in (a, b).

Front

What does it mean for a function to have a derivative?

Back

A function has a derivative at a point if it has a defined slope (instantaneous rate of change) at that point.

Front

What is the difference between average velocity and instantaneous velocity?

Back

Average velocity is the total displacement divided by the total time, while instantaneous velocity is the velocity of an object at a specific moment in time.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4