11The question does not say f(x) is a polynomial in 'x'!!
1) Let f(x) be a polynomial satisfying f(0)=2, f' (0)=3 and f'' (x)=f(x). Then find f(4).
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62for a polynomial (of finite degreee!) The f"(x)=f(x) is not posible!! unless f(x)=0
As far as I know we talk of polynomials as having Finite degree!
I will be very interested to see the solution! (Or even the answer!)
112) Is there any other value of f(4) also possible,if " f(x) be a polynomial " is not mentioned in the question??
11I just tried to make the question more clear!! since I know the answer(but not the solution).
62rkrish your statement to me makes no sense... (sorry!)
Bcos when we talk about a polynomial it has to be a polynomial in something..
Otherwise i can say that (sinx)2 is a polynomial in "sin x"
And similarly for almost any function!!!
1let f(x) = a0 + a1x + a2x2 + a3x3 + .........+ anxn
f(0) = a0 = 2
f'(x) = 0 + a1 + a2x1 + 3a3x2 + .........+ n anxn-1
=> f'(0) =a1 = 3
=> f"(x) = 0 + 0 + a2 + 6a3x + ..........+ n(n-1)xn-2
=> f"(0) = f(0) => a2 = a0 = 2 .
so we finally have someting like :
p(x) = 2 + 3x + 2x2 + .......
1this question can be corrected by saying f"(x) = f(0)
and then the answer wud be 30 !
i.e; when f(x) = x2+3x+2
11The language of the question is the same as given.
Well,the ans. given is (5e8-1)/(2e4)
Pls.try to prove it.
11Thats what...in the question its metioned that " f(x) is a polynomial " but the ans given is exponential !! [7][7]
1okay so the conclusion can be thus drawn !!.... the question makes no sense until n unless f"(x) = f(0) !!