Graphs of functions and their derivatives

Front

What does it mean when a graph is increasing?

Back

A graph is increasing when the function's output values rise as the input values increase. This implies that the derivative of the function is positive.

Front

What does it mean when a graph is decreasing?

Back

A graph is decreasing when the function's output values fall as the input values increase. This implies that the derivative of the function is negative.

Front

What is the relationship between a function and its derivative at a maximum point?

Back

At a maximum point, the derivative of the function is zero (f'(x) = 0) and changes from positive to negative.

Front

What is the relationship between a function and its derivative at a minimum point?

Back

At a minimum point, the derivative of the function is zero (f'(x) = 0) and changes from negative to positive.

Front

How can you determine where a function is increasing or decreasing using its derivative?

Back

A function is increasing where its derivative f'(x) > 0 and decreasing where f'(x) < 0.

Front

What does a positive derivative indicate about the graph of a function?

Back

A positive derivative indicates that the graph of the function is increasing.

Front

What does a negative derivative indicate about the graph of a function?

Back

A negative derivative indicates that the graph of the function is decreasing.

Front

What is the significance of a zero derivative?

Back

A zero derivative indicates a potential maximum or minimum point on the graph of the function.

Front

If f'(x) > 0 on an interval, what can be said about f(x) on that interval?

Back

If f'(x) > 0 on an interval, then f(x) is increasing on that interval.

Front

If f'(x) < 0 on an interval, what can be said about f(x) on that interval?

Back

If f'(x) < 0 on an interval, then f(x) is decreasing on that interval.