Inflection Point, Concave Up/Down, Interval

Front

What is the definition of concave up?

Back

The definition of concave up is a curve that is curved upwards.

Front

What is the definition of concave down?

Back

The shape of a curve that is curved downward.

Front

What does an inflection point indicate on a graph?

Back

An inflection point indicates where a curve changes from concave up to concave down or vice versa.

Front

What is the relationship between the second derivative and concavity?

Back

If the second derivative is positive, the function is concave up; if negative, the function is concave down.

Front

How do you determine the intervals of concavity?

Back

To determine intervals of concavity, find the second derivative and analyze its sign over the intervals.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using parentheses and brackets to indicate whether endpoints are included.

Front

What does the interval notation \( (-\infty, 8) \) represent?

Back

It represents all real numbers less than 8, not including 8.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on its orientation.

Front

How can you identify a maximum or minimum vertex in a parabola?

Back

If the parabola opens upwards, the vertex is a minimum; if it opens downwards, the vertex is a maximum.

Front

What is the significance of a maximum point in a function?

Back

A maximum point indicates the highest value of the function within a given interval.