First Derivative Test

Front

What is the first derivative test used for?

Back

The first derivative test is used to determine the relative extrema of a function.

Front

What is a local maximum in the context of the first derivative test?

Back

A local maximum is a point on a function where the derivative changes from positive to negative.

Front

What is the relationship between increasing intervals and positive first derivative?

Back

As the intervals between values increase, the first derivative is positive.

Front

What are increasing intervals in the context of the first derivative test?

Back

Intervals where the derivative is positive.

Front

How do you find critical points using the first derivative test?

Back

To find critical points using the first derivative test, follow these steps: 1. Find the first derivative of the function. 2. Set the first derivative equal to zero and solve for x to find the critical points. 3. Determine the sign of the first derivative on either side of each critical point. 4. If the sign changes from positive to negative, the critical point is a local maximum. If the sign changes from negative to positive, the critical point is a local minimum. If the sign does not change, the critical point is an inflection point.

Front

What does it mean if the first derivative is positive on an interval?

Back

The function is increasing on that interval.

Front

What does it mean if the first derivative is negative on an interval?

Back

The function is decreasing on that interval.

Front

What is a critical point?

Back

A critical point is a point on the graph of a function where the first derivative is zero or undefined.

Front

What is the significance of a critical point where the first derivative changes from negative to positive?

Back

It indicates a local minimum.

Front

What is the significance of a critical point where the first derivative changes from positive to negative?

Back

It indicates a local maximum.