Derivative Graphs

Front

What does it mean when a graph is increasing?

Back

A graph is increasing when the function values rise as the input values increase, indicating that the derivative is positive.

Front

What does it mean when a graph is decreasing?

Back

A graph is decreasing when the function values fall as the input values increase, indicating that the derivative is negative.

Front

What is the relationship between a function and its derivative when the function has a local maximum?

Back

At a local maximum, the derivative changes from positive to negative, indicating a stationary point.

Front

What is the relationship between a function and its derivative when the function has a local minimum?

Back

At a local minimum, the derivative changes from negative to positive, indicating a stationary point.

Front

What does a zero derivative indicate about a function at a point?

Back

A zero derivative indicates a stationary point, which could be a local maximum, local minimum, or a point of inflection.

Front

How can you determine if a function is concave up or concave down using its derivative?

Back

If the derivative is increasing, the function is concave up. If the derivative is decreasing, the function is concave down.

Front

What is a sign chart for a derivative?

Back

A sign chart for a derivative shows the intervals where the derivative is positive, negative, or zero, helping to analyze the behavior of the original function.

Front

What does it mean if the derivative of a function is positive on an interval?

Back

If the derivative is positive on an interval, the function is increasing on that interval.

Front

What does it mean if the derivative of a function is negative on an interval?

Back

If the derivative is negative on an interval, the function is decreasing on that interval.

Front

What is the significance of points where the derivative is zero?

Back

Points where the derivative is zero are potential locations for local maxima, local minima, or points of inflection.