Thread: Critical x help

How do I show that a cubic function can have a two, one, or no critical numbers? And what are examples of them?

Also, how many local extreme values can a cubic function have?

Any help appreciated -- thanks!

Originally Posted by amma0913

How do I show that a cubic function can have a two, one, or no critical numbers? And what are examples of them?

What is the derivative of a cubic polynomial? Aha...and now, what are the options for the roots of this derivative?
There you go!

Also, how many local extreme values can a cubic function have?

Read above and think

Tonio

Any help appreciated -- thanks!

.

What is an example of a quadratic function with one critical x?

Thanks

Well, what is the definition of "critical point"?

What do you know about the derivative of a quadratic function?

(Or did you mean "cubic" function as in your first post? In that case what do you know about the derivative of a cubic function?)