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.
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.
Hello, kwtolley!
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!