Unit 5 AB Calc Review for Flashcard

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 point c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).

Front

When is a particle's speed decreasing?

Back

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

Front

What does it mean if a function has a local maximum?

Back

A function has a local maximum at a point if the function value at that point is greater than the function values at nearby points.

Front

What is an absolute maximum?

Back

An absolute maximum is the highest value of a function over its entire domain.

Front

What is the significance of a sign chart for f'(x)?

Back

A sign chart for f'(x) helps determine where a function is increasing or decreasing, and can indicate local maxima and minima.

Front

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

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) > f(x2).

Front

What is the relationship between velocity and acceleration?

Back

Velocity is the rate of change of position, while acceleration is the rate of change of velocity. Their signs indicate whether the speed is increasing or decreasing.

Front

How do you determine if a critical point is a local minimum?

Back

A critical point is a local minimum if f'(x) changes from negative to positive at that point.

Front

What is the difference between local and absolute extrema?

Back

Local extrema are the highest or lowest points in a small neighborhood, while absolute extrema are the highest or lowest points over the entire domain.

Front

What does it mean if a function is continuous on an interval?

Back

A function is continuous on an interval if there are no breaks, jumps, or holes in the graph of the function over that interval.