Interpolate maximum of a dataset

Question

I have a dataset that I know fits a graph approximately like:

I know that the region beyond the maximum will be approximately double the region before it but apart from that I don't know much about it.

So what I would like to know is how to find the x value of the maximum of the curve.

Answer 1

How your fit looks like? Is it a concrete function? If yes, let it be $f(x)$. Denote by $M$ the abscissa of a maximum on that curve. Then we have such equation:

$$ 2\int_{\min}^M f(x)\text{d}x=\int_{\min}^{\max} f(x)\text{d}x. $$

Try to solve this equation wrt. the unknown $M$.