Graphs of functions and their derivatives

Front

What does it mean if a function's derivative is negative?

Back

The function is decreasing.

Front

What is the derivative of a function?

Back

The instantaneous rate of change of the function.

Front

When a graph is increasing, what can be said about its derivative?

Back

The derivative is positive.

Front

When a graph is decreasing, what can be said about its derivative?

Back

The derivative is negative.

Front

What does the slope of a tangent line to a curve represent?

Back

The derivative of the function at that point.

Front

If the derivative of a function is zero, what does that indicate?

Back

The function may have a local maximum, minimum, or a point of inflection.

Front

What is the relationship between a function and its derivative in terms of increasing and decreasing behavior?

Back

If the derivative is positive, the function is increasing; if negative, the function is decreasing.

Front

How can you determine the maximum or minimum points of a function using its derivative?

Back

By finding where the derivative is zero or undefined.

Front

What does a positive derivative indicate about the function's graph?

Back

The graph is rising.

Front

What does a negative derivative indicate about the function's graph?

Back

The graph is falling.