Question

Help with Linear Algebra Question Please.

Find the cubic polynomial f(x) such that f(2)=-13, f'(2)=-11, f''(2)=-10, and f'''(2)=-6.
f(x)= ___ x^3+ ____x^2+____ x+ ____.

I know to find the integral and i found these

(2,-13)
f(2) = -11x
f(2) = -5x^2
f(2) = -x^3

But i'm confused of what to do next. Thanks a lot

Answer 1

\(f(x)=ax^3+bx^2+cx+d\)
\(f'(x)=3ax^2+2bx+c\)
\(f''(x)=6ax+2b\)
\(f'''(x)=6a\)
now change x by 2 and solove system for a,b,c,d

Answer 2

so

8a + 4b + 2c + d = -13
12a + 4b + c = -22
12a + 2b = -20
6a=-8?

Answer 3

well i know a is -1 cause i guessed :3 but it seems like it's wrong in this case

Answer 4

f'''(2)=-6.
so
6a=-6
a=-1

Answer 5

it's right

Answer 6

how did you get -6?

Answer 7

it's written in your problem

Answer 8

"Find the cubic polynomial f(x) such that f(2)=-13, f'(2)=-11, f''(2)=-10, and f'''(2)=-6. "

Answer 9

aaaah okay. so finding the integral doesn't have to do with this

Answer 10

so the system will be:
8a+4b+2c+d=-13
12a+4b+c=-11
12a+2b=-10
6a=-6
you don't need integral

Answer 11

ok. i get it. thanks a lot!

Answer 12

yw

Answer 13

so a = -1 b = 1 c = -3 and d = -3 and they're right :) thank you again!

Answer 14

yw