Concavity Flashcard

Front

What does it indicate when f'(x) changes from negative to positive?

Back

There is a minimum.

Front

What does it indicate when f'(x) changes from positive to negative?

Back

There is a maximum.

Front

How do you identify critical points of a function?

Back

Set f'(x) = 0 and solve for x.

Front

What is a sign chart used for in calculus?

Back

To determine the intervals of increase and decrease of a function.

Front

What are relative minimum values?

Back

Points where the function value is lower than the values of the function at nearby points.

Front

What is the first derivative test?

Back

A method to determine local extrema by analyzing the sign of f'(x) around critical points.

Front

What is a local maximum?

Back

A point where the function value is higher than the values of the function at nearby points.

Front

What is the second derivative test?

Back

A method to determine concavity and local extrema by analyzing the sign of f''(x).

Front

What does f''(x) > 0 indicate about the function?

Back

The function is concave up.

Front

What does f''(x) < 0 indicate about the function?

Back

The function is concave down.