11ax does not satisfy for f'(0) as bhaiyya pointed out
so what is the function then [7]no need for this
Let f (x + y) = f (x) f (y) for all x and y. Suppose that f (3) = 3 and f '(0) = 11. Then f ' (3) is given by :
opts are : 22,33,44, none of these....
Ans:
I'm getting 33 but the ans reads none of thes
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35 Answers
33are yaar .... aisa thode hi hai...
ans sab method se ana chahiye... ye maths hai chem nahi..[3]
i think theres no such continuous and differentiable function...
:P
33lol... mera dimag aaj ghumne gaya hai....
phir se banate hai suru se...
21ani already pointed it.... :(
but abhishek then ur functn cant b λe^(kx).....
i guess this type of sums shall b done widout assumin a functn....
ie the nishant sir has solved, makin use of the diff properties n given values of f(a)
11
24yes it does not satisfy.........[7].......i think may be this part of question is wrong..[12].....
vaise bhi.......magic math has already written.."BUT ther r a NO. OF mistakes in it...."[1]
11no need to find the function so proceed like nishant bhaiyya has done and get the answer (:( which he says is wrong)
24uffffffff[2]..............it was all over in 4th post.........and i started it again[9]
21hmmmm....
manish sir! in ur post da equality sign shud not equal to sign ne coz RHS we λ2 and in LHS sirf λ
33Eureka is also right ax only satisfies f(x+y)=f(x)f(y) but it doesn't satisfies....other condition f'(0)=11
21I JUS LOVE THIS STATEMENT :
"ans sab method se ana chahiye... ye maths hai chem nahi"
21BUT HEY AB IF f'(0) exists n is equal to 11 it means its derivative exists.........
unless u consider it is non differentiable at x=3; which wud b toooo hard on the paper setter thodi daya karo us becherre par... [1]
11"ans sab method se ana chahiye... ye maths hai chem nahi"
yes true but what is the method here other than bhaiyyas
checking for functions isnt a method
21subhash my connotation was to the statement in general.....
in this questn mayb ther doesnt existr a method.....
but the thot that in che n maths wenever 2 diff meth of solvign same sum exist then in math both lead to da same ans which is rarely the case in CHE....
SORRY CHEM LOVERS..... but i feel dats a fact
62There is no mistake in my solution..
because if you see closely, it is given differentiable at 3 just because it says f'(3) = something
and f'(0)= something else.
Remove x from my solution.. replace it by 3..
then do all the steps that I did..
It will work.
24sorry to everyone........i made a compelete blunder.............Yes Nishant Sir is correct...............GOIIT IS WRONG....
1357I have a little doubt
for f(x)=ax, is the condition f'(0)=11 true??
62oh din read the 2nd part of ur message..
Even I am getting 33...
Where is the question from :(
1its actually frm goiit test carnival.....(4 IIT JEE)
BUT ther r a NO. OF mistakes in it....
abt 10 in BITSSAT paper alone
24it is none of these dear...........
it is Cauchy'2 2nd equation
=> f(x)=ax
f(3)=3 =>a3=3 =>a=31/3
we have to find f'(3)
so first get f'(x)=axloga
=>f'(3)=31/3 (3)log31/3
=>f'(3)=log3 [1]
39ya right eureka. AND MAGIC MATH U REMEMBER THIS, THE FUUNCTION SATISFYING THE GIVEN GIVEN EUATION IS ax.
sry
11But bhaiya just proved convincingly that it is 33.......so whose mistake is it...........bhaiya's and Magic Math's or goiit's?
24i can only say that ans is log3....[2].......
i will try t ofigure out any calculation mistake here....[12]
62f(x)=f(x).f(0)
so f(0)=1
f(x+h)-f(x)=f(x){f(h)-1}
f(x+h)-f(x)=f(x){f(h)-f(0)}
divide by h and take limit as h tending to zero..
f'(x)=f(x).f'(0)
so f'(3)=3.11=33
33Function is...
y=λekx where λ,k are constant..
where λk=11 and 3=λe3k..
11Arey yaar. Is proof to be given in accordance to the answer or the other way round?