Increased Accuracy in RobustNewtonRaphson.TryFindRoot causes Failure to find Roots

[mio991]

I have a function to find extrema in sampled data using root finding.

I put the code here: https://gist.github.com/mio991/e4e2edb0a1fd9a8d10f175f70eec1115.

I am trying to find the extrema of this function (x-20)*(x-80)*(x-120)*(x-150)*(x-190).

If I Increase the Accuracy from 1e-6 to 1e-8 for example the Function fails to find the root at 39.073. It sets root to 39.07... but returns false.