Max/Min

Front

What is the definition of Absolute Minimum?

Back

The Absolute Minimum of a function is the lowest point over its entire domain. It is the smallest value that the function can take.

Front

What is the definition of Absolute Maximum?

Back

The Absolute Maximum of a function is the highest point over its entire domain. It is the largest value that the function can take.

Front

What is a Relative Maximum?

Back

A Relative Maximum is a point where the function value is higher than the values of the function at nearby points, but not necessarily the highest overall.

Front

What is a Relative Minimum?

Back

A Relative Minimum is a point where the function value is lower than the values of the function at nearby points, but not necessarily the lowest overall.

Front

How do you find Absolute Maxima and Minima?

Back

To find Absolute Maxima and Minima, evaluate the function at critical points (where the derivative is zero or undefined) and at the endpoints of the interval.

Front

What is the difference between Absolute and Relative Extrema?

Back

Absolute Extrema refer to the highest or lowest points over the entire domain, while Relative Extrema refer to the highest or lowest points in a specific interval.

Front

What does it mean if a function has no Absolute Minimum?

Back

If a function has no Absolute Minimum, it means that the function does not reach a lowest value within its domain, often due to the function approaching negative infinity.

Front

What does it mean if a function has no Absolute Maximum?

Back

If a function has no Absolute Maximum, it means that the function does not reach a highest value within its domain, often due to the function approaching positive infinity.

Front

What is a critical point?

Back

A critical point of a function is a point in its domain where the derivative is zero or undefined, which may indicate a local maximum or minimum.

Front

How can you determine if a critical point is a maximum or minimum?

Back

You can use the First Derivative Test or the Second Derivative Test to determine if a critical point is a maximum or minimum.