A community for students.
Here's the question you clicked on:
 0 viewing
dougliedigg
 2 years ago
Find a polynomial equation of degree 3 such that f(0)=31, f'(1)=4, f"(2)=2, and f'"(3)=6.
dougliedigg
 2 years ago
Find a polynomial equation of degree 3 such that f(0)=31, f'(1)=4, f"(2)=2, and f'"(3)=6.

This Question is Closed

Cutler
 2 years ago
Best ResponseYou've already chosen the best response.0You know that the function has to be f(x) = ax^3 + bx^2 + cx + 31. Next you know that the f'(x) = 3ax^2 + 2bx + c, and that f'(1) = 4, so we know that 3a + 2b + c = 4 Then f''(x) = 6ax + 2b, and f''(2) = 2, Therefore 12a + 2b = 2 Last but not least f'''(x) = 6a, and f'''(3) = 6, and with that you know that a = 1 Go back to 12a + 2b = 2, plug in a, and you get 12 + 2b = 2, therefore b = 5 Now you can go back to 3a + 2b + c = 4, plug in, and you will get 3 + (10) + c = 4, and c = 11. Finally, you get the equation that f(x) = x^3  5x^2 + 11x + 31

dougliedigg
 2 years ago
Best ResponseYou've already chosen the best response.0thanks so muchhh :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.