I have a requirement for a function which can be modeled as following
Function $ y = f(x) $ which satisfies the following conditions.
There are 3 real numbers a,b,c on number line ST a < b < c and
f(x) is a continuous, differentiable curve, in the range x $ \epsilon $(a,c)
$$ (b-a)/(c-b)= 2/3 $$
$$ f(x) > 0, x \epsilon (a,c) $$
$$ \int_{a}^{b} f(x) dx = 7/3 \int_{b}^{c} f(x) dx$$
I need to find the function f, and values a,b,c.
I tried several knows functions like $ x^{2} $, $ e^{x} $ but none of them seem to satisfy this. Can you help me find this?
PS: Just to be clear, I don't care about the values of f outside (a,c)
The constant function $f(x)=\frac{7}{2}$ will do the job.