Question

antiderivative problem

Answer 1

does F'(0) means that f wont be included in the sum

Answer 2

i'm not sure....

Answer 3

@butterflydreamer

Answer 4

well first find f' from f''

Answer 5

can u show me how?

Answer 6

please :)

Answer 7

\[f''(x)=6x+6\sin x \Longrightarrow \int 6x+6\sin x dx=f'(x) \\ 3x^2-6\cos x+c=f'(x) \]

Answer 8

so i do the anti derive. again?

Answer 9

through the givens we can find c
f'(0)=3(0)-6cos0+c=3
-6+c=3
c=9
so \[f'(x)=3x^2-6\cos x+9\]

Answer 10

ok

Answer 11

yes you have to apply the anti derive one more time to get to f

Answer 12

so i got x^3 - 6sinx

Answer 13

then i'd need the c I'm guessing?

Answer 14

x^3-6sinx +c
then find the c again

Answer 15

yah you are given that f(0)=3

Answer 16

it it 9 then?

Answer 17

wait no

Answer 18

no solve don't just guess!

Answer 19

3

Answer 20

cuz u plug in zero into the equation and then set it equal to 3?

Answer 21

yes

Answer 22

exactly!

Answer 23

well ...

Answer 24

I think someone forgot to integrate 9 earlier

Answer 25

what did you get for f(x)
given \[f'(x)=3x^2-6\cos x+9\]

Answer 26

i got x^3 - 6sinx

Answer 27

why ignore the 9?

Answer 28

oppss

Answer 29

got it thanks!!

Answer 30

recall (9x+d)'=(9x)'+(d)'=9+0=9

so you get f(x)= x^3-6sin(x)+9x+d
then you find the constant d using f(0)=3

Answer 31

eh i forgot the constant 9 too :)
got catch @freckles

Answer 32

My kitty told me about it.

Answer 33

good catch i mean :)
kitty haha