CONCAVITY, & INCREASING /DECREASING RATES FUNCTIONS

Front

What does it mean for a function to be negative?

Back

A function is negative when its values are below the x-axis.

Front

What is concavity in relation to a function?

Back

Concavity refers to the direction the curve of the function opens: concave up (like a cup) or concave down (like a frown).

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the function values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as x increases, the function values decrease.

Front

How can you determine if a function is concave up?

Back

A function is concave up if its second derivative is positive or if the slope of the tangent line is increasing.

Front

How can you determine if a function is concave down?

Back

A function is concave down if its second derivative is negative or if the slope of the tangent line is decreasing.

Front

What is the average rate of change of a function?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in x over that interval.

Front

What is a positive rate of change?

Back

A positive rate of change indicates that as one variable increases, the other variable also increases.

Front

What is a negative rate of change?

Back

A negative rate of change indicates that as one variable increases, the other variable decreases.

Front

What does it mean for a function to be concave up and increasing?

Back

A function is concave up and increasing when the function's values are rising and the rate of increase is itself increasing.