APPC Review A for 1.1-1.6

Front

What does it mean for a function's rate of change to be positive and decreasing?

Back

It means that the function is increasing, but the rate at which it increases is slowing down.

Front

Define 'decreasing' in the context of a function.

Back

A function is decreasing on an interval if, as x increases, the function's value decreases.

Front

What does 'concave up' mean for a function's graph?

Back

A graph is concave up if it opens upwards, indicating that the slope of the tangent line is increasing.

Front

What does 'concave down' mean for a function's graph?

Back

A graph is concave down if it opens downwards, indicating that the slope of the tangent line is decreasing.

Front

How can you determine if a function is decreasing on an interval?

Back

By analyzing the first derivative of the function; if the derivative is negative over that interval, the function is decreasing.

Front

What is the significance of the second derivative in determining concavity?

Back

The second derivative indicates concavity; if it is positive, the function is concave up, and if negative, concave down.

Front

What does it mean for a function to be decreasing at a decreasing rate?

Back

It means that while the function is still decreasing, the amount by which it decreases is getting smaller.

Front

How do you identify intervals where a function is concave up?

Back

Find where the second derivative is positive.

Front

What is the relationship between the first and second derivatives in determining increasing/decreasing behavior?

Back

The first derivative indicates increasing/decreasing behavior, while the second derivative indicates concavity.

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's value also increases.