Find the third degree polynomial whose graph is shown in the figure. My answer is f(x)= 1/4x^3 - 1/4x^2 +2x+2, but I'm not sure. Thanks for checking my answer.

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- July 5th 2006, 09:08 AMkwtolleyThird degree
Find the third degree polynomial whose graph is shown in the figure. My answer is f(x)= 1/4x^3 - 1/4x^2 +2x+2, but I'm not sure. Thanks for checking my answer.

- July 5th 2006, 09:22 AMCaptainBlackQuote:

Originally Posted by**kwtolley**

RonL - July 5th 2006, 10:01 AMkwtolleycubic
The graph I put together is off some, as for being cubed or not thats why I'm asking. Some of my home work is hard, thats why I ask because I like to see how I messed up my answer, and checking the instructor also. Instructor/teachers can make mistakes just like all of us.

- July 5th 2006, 02:26 PMSoroban
Hello, kwtolley!

Quote:

Find the third degree polynomial whose graph is shown in the figure.

My answer is: , but I'm not sure.

We have a*big*problem . . .

A cubic function, , has__four__constants to determine,

. . but we are given only__three__facts.

[1] The point is on the graph.

[2] The point is on the graph.

[3] There is a critical point at

Since

. . The function (so far) is: .

Since

. .**[1]**

The derivative is: .

Since**[2]**

Add [1] and [2]: .

Substitute into [2]: .

Therefore: .

And, if there is no more information, that's the best we can do.

Edit: corrected that silly "3" . . . Thanks for the heads-up! - July 5th 2006, 03:48 PMQuickQuote:

Originally Posted by**Soroban**

- July 6th 2006, 08:03 AMkwtolleythanks
thanks for checking my answer I reworked it and got the right answer.