Question

Fill in the blanks:

1) An absolute maximum or absolute minimum is called an ______________

2) Theorem: Extreme Value Theorem

A function that is _________ on a ___________ interval [ a , b ] has both an ______________ and an absolute minimum on that interval.

3) Theorem: Second-Derivative Test for Absolute Extrema on an Interval

Let f be continuous on an interval I from a to b with only one critical number c in ( a , b ).

If f ′ ( c ) = 0 and f ″ ( c ) > 0, then f ( c ) is the _________ of f on I.

If f ′ ( c ) = 0 and f ″ ( c ) < 0, then f ( c ) is the __________ of f on I.

Answer 1

) An absolute maximum or absolute minimum is called an -----absolute extrema----

2) Theorem: Extreme Value Theorem

A function that is ------continuous------ on a ------closed------ interval [ a , b ] has both an -----absolute maximum------ and an absolute minimum on that interval.

3) Theorem: Second-Derivative Test for Absolute Extrema on an Interval

Let f be continuous on an interval I from a to b with only one critical number c in ( a , b ).

If f ′ ( c ) = 0 and f ″ ( c ) > 0, then f ( c ) is the -----local minimum ------ of f on I.

If f ′ ( c ) = 0 and f ″ ( c ) < 0, then f ( c ) is the ------local maximum-------- of f on I.