Question

Find f(3)

Answer 1

\[\LARGE f(2x)=f'(x).f"(x)\]

Answer 2

I replaced x with 3/2

Answer 3

\[\LARGE f(3)=f'(\frac{3}{2}) \times f"(\frac{3}{2})\]
m stuck here

Answer 4

@ganeshie8

Answer 5

substite for \[f(x)=e^{ax}\]

Answer 6

find what the f(2x) is than what f'(x) is and f''(x)

Answer 7

put that in equation and solve for a

Answer 8

then substitute that a and 3 instead of x and you should come up with the right answer

Answer 9

why e^ax?

Answer 10

i predict that this function could satisfy my equation

Answer 11

What value did you find?

Answer 12

i cudn't find it

Answer 13

not getting the correct answer,confused

Answer 14

well if f(x)=e^ax what is f(2x)?

Answer 15

e^2ax

Answer 16

yes, what about the first and second derivative of f(x)?

Answer 17

2e^2ax and 4e^2ax

Answer 18

a is also constant, but you tried to calculate derivatives of e^2ax but in equation you have to take derivatives of f(x) so these are derivatives of e^ax

Answer 19

yes

Answer 20

so first derivative is a*e^ax and second is a^2*e^ax. Substitute them to equation

Answer 21

and solve for a

Answer 22

I think u missed 2 and 4

Answer 23

no, we take derivative of
\[e^{ax}\]

Answer 24

\[\LARGE e^{2ax}=ae^{ax} \times ae^{ax} \]

Answer 25

\[e^{ax}=ae^{ax}*a^2e^{ax}=a^3*e^{ax+ax}=a^3*e^{2ax} \rightarrow a=1\]

Answer 26

im sorry,a=1?

Answer 27

yeah..

Answer 28

so your function f(x) is simply e^x

Answer 29

so f(x)=e^x only

Answer 30

so f(3) =?

Answer 31

e cube? :/

Answer 32

right :)

Answer 33

Options:
A)4
B)12
C)15
D)None of these

Answer 34

I think none of these

Answer 35

it is 12 ....

Answer 36

how come?

Answer 37

dont know

Answer 38

Just insert the 3 to the places in which the x belongs.

Answer 39

I guess someone didnt read the question

Answer 40

So the confusing part can be when it shows the f(2x). Since the rule is to insert the 3 to x, what you just need to do is multiply the 2 and 3 which will evaluate to 6 making it f(6)

Answer 41

read my first reply

Answer 42

What do you mean?

Answer 43

x->3/2

Answer 44

So you're saying that you should input 3/2 to x?

Answer 45

yes

Answer 46

But that's not how I would evaluate the problem because it is the same thing as 2(3)

Answer 47

What I mean to say is that you have to multiply the 2 and 3 since the variable x is right next to 2.

Answer 48

That's would be my first cue towards solving this procedure.

Answer 49

there are many infinitely solutions for the functional equation\[f(2x)=f'(x) f''(x)\]i'd probably say the problem must be something else, \(f\) will be a polynomial i think through ur options

Answer 50

i got \(12\) with considering \(f\) as a polynomial :)