Question

Use the given information about f ' and f '' to find f(x)
f " (x)=2 f '(2)=5 f(2)=10

Answer 1

integrate ^^

Answer 2

correct sis

Answer 3

integrate f ' (2) ?

Answer 4

Hint :-
\(f'(x)=\int f''(x) \)

Answer 5

yes

Answer 6

nope not f'(2)
start with integrate f''(x)=2
do you know how to do that?

Answer 7

ok so f(x)=2x correct?

Answer 8

that can't be it because f(2) would not be 10

Answer 9

nope , check the hint above
\(f'(x) = \int f''(x) +c \)

Answer 10

I really don't know how to do these problems. I do better with functions.

Answer 11

so u have
\(f'(x) = 2x+c\)
since you know f'(2)=5 try to find c

Answer 12

ohkk :)
only u are agree to this ?

Answer 13

5=10+c

Answer 14

ok I wil try

Answer 15

c=1 ?

Answer 16

haha not try lol
i wont continue unless ur agree to that ,so shall we start over ?

Answer 17

yes

Answer 18

good :D
so if i asked you whats the derivative of f(x) what do you say ?

Answer 19

I truly am not interested in the solution. I really am going for learning how to do the problem so that I can do other similar problems and do well on my exam

Answer 20

derivative of 2x is 2

Answer 21

no i meant any f(x) , u say derevative of f(x) is f'(x) ok ?

Answer 22

well , i would like to teach you :D

Answer 23

ok I am sorry I thought we had established that it was 2x but yes

Answer 24

yes the derivative of f(x) is f ' (x)
the derivative of f '(x) is f " (x)

Answer 25

good :)
now you know that integrate is the inverse of derevative right ?

Answer 26

yes also, known as the antiderivative

Answer 27

cool :D

Answer 28

now what is the integration of f''(x) ?
since we know that derevative f'(x) is f''(x) ?

Answer 29

f ' (x)

Answer 30

yep your almost correct , we need c constant to add
since
(f'(x)+c)=f''(x) + c'
and since c is constant then c' is zero
Hence :-
(f'(x)+c)=f''(x)

so we are not sure if integrate f''(x) is exactly f'(x) it might have a constant addition

agree to this ?

Answer 31

so we say
\(\int f''(x) = ?\)

Answer 32

need a moment to think

Answer 33

ok take ur time :D

Answer 34

sorry had to chase off a woodpecker (he was on my house)

Answer 35

but the integral of f "(x) should just be f '(x) + c as you stated earlier

Answer 36

lol i like that bird :P
ur correct , so understood ?

Answer 37

yes but still not sure what to do
ok I will write what I think I should do and you can correct me. I am sure I am incorrect

Answer 38

ok ^^

Answer 39

f(2)=10 is just a point (2,10) this just gives me a location
f ' (2) =5 means that when I take the first derivative and sub 2 I should get 5 and this tells me that the function is increasing since 5 is a positive number or f '(2)>0
f"(x)=2 tells me that the function is concave up

Answer 40

ok am I trying to find the function itself using the two values given f(2)=10 and f'(2)=5?
I am not even sure I understand the directions

Answer 41

well
check this
\(f'(x) =\int f''(x) +C \)
right ?
then
\(f'(x) =\int 2 dx +C \)
can you find f'(X) now with respect to c ?

Answer 42

f '(2)=2x +c
5=2(2)+c
5=4+c
1=c
so 2x+c
2x+1
so I just need to integrate that and that is my f(x) correct?

Answer 43

x^2 +x is my original function
ok let me check all of the given information
x=2 2^2+2 =4+2=6 so f(2)=10 does not work out
guess I am still not sure

Answer 44

ok for f'(x) ur correct
f'(x)=2x+1
:D
now the same idea with f(x) dnt forget to add c
\(f(x)=\int f'(x) +c\)

Answer 45

ok then let me write on my paper and think this through

Answer 46

ohkkk :)

Answer 47

ok my function is x^2+x+4
so let me check if x = 2 2^2+2+4=4+2=4=10 so f(2) = 10
f ' (x) = 2x+1 if f"(2)=2(2)+1=5 so that checks out as well

Answer 48

you are correct !

Answer 49

^^ well done

Answer 50

thanks I have another one to tackle but I think I will do it later, gotta go run errands and chase off my woodpecker. I really do have an annoying bird attacking my house.
btw Thanks for helping me understand this problem better.

Answer 51

np :)
ur wlc
PS :- don't hurt that bird ok :P

Answer 52

no just chasing it off. They always go to the other houses that are made of wood. Mine is not wood, just fake wood. Once they realize this, they leave anyways.

Answer 53

huh ok :P
good luck !