Maximum and Minimum (CFU)

Front

What is a Local Minimum?

Back

A point in a function where the value is lower than all nearby points, but not necessarily the lowest overall.

Front

What is an Absolute Minimum?

Back

The lowest point in the entire function, where no other point has a lower value.

Front

What is a Local Maximum?

Back

A point in a function where the value is higher than all nearby points, but not necessarily the highest overall.

Front

What is an Absolute Maximum?

Back

The highest point in the entire function, where no other point has a higher value.

Front

How do you identify a maximum or minimum value in a graph?

Back

Look for the highest or lowest points on the graph, where the slope changes direction.

Front

What does it mean if a function has a maximum at a certain point?

Back

It means that at that point, the function reaches its highest value compared to nearby points.

Front

What does it mean if a function has a minimum at a certain point?

Back

It means that at that point, the function reaches its lowest value compared to nearby points.

Front

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

Back

If the first derivative changes from positive to negative at a point, it's a maximum; if it changes from negative to positive, it's a minimum.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on its orientation.

Front

What is the difference between local and absolute extrema?

Back

Local extrema are the highest or lowest points in a small region, while absolute extrema are the highest or lowest points in the entire function.