1edited ........no mistakes in the question
F(x)= 0∫x f(x)dx,
x ≥ 0, f(x)≥ 0, f(x)≤C - F(x). find f(x)
plz tell how to solve this ................
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10 Answers
11dude have a close look at the question
u will find that
F'(x)=f(x)
now it is given that f(0+)≥0
and
F(x)+f(x)≤C
or
F'(x)≤-f'(x)
as F'(x)=f(x)
we get
f(x)+f'(x)≤0
now when x≥0 u said f(x)≥0 so f'(x) have to be negative value equal to or greater than f(x)
this implies that the derivative of the function is -ve or 0
So for sure u have a function satisfying the above equations as a 0 function.
for any other case we will have to look into deeply.
or it could be like
but here the problem lies in the fact that when x→0 then its slope tends to ∞ so the conditions above becomes absurd.
I am only able to find a constant 0 function.
Please tell if functions r required .
9f(x) = Ae-x where A <=C is also possible
and see its impossible to find f(x) exactly
infinite solutions exist !!!!!!!