Chapter 4.3: Maxima and Minima

Question 1

What is a local maxima?

Answer 1

A maximum within a restricted domain, especially a point on a function whose value is greater than the values of all other points near it.

Question 2

What is an absolute extremum?

Answer 2

An absolute extremum (or global extremum) of a function in a given interval is the point at which a maximum or minimum value of the function is obtained. Frequently, the interval given is the function’s domain, and the absolute extremum is the point corresponding to the maximum or minimum value of the entire function.

Question 3

What is an absolute minimum?

Answer 3

the smallest value that a mathematical function can have over its entire curve

Question 4

What is a local minimum?

Answer 4

A local minimum, also called a relative minimum, is a minimum within some neighborhood that need not be (but may be) a global minimum.

Question 5

What is a critical point?

Answer 5

Where the derivative is equal to zero or DNE.