I am currently trying to finish an assignment regarding Newton-Raphson method. Anyone able to explain an example to me? The function $f(x) = \sin(x) + \sin(\frac{10x}{3})$ is shown on the picture. The red dot is the starting point and the cross is a local extrema found by using the NR method. My question is why isn't the cross on the local extremas near the starting point, specifically where $x \approx 1.5$ and $x \approx 0.5$ which is visible on the picture. Why did the point end up where it did and passed two extremas on its way? Could this be an implementation issue, or is this how it's supposed to be ?

![Local extrema found using the NR method](https://i.stack.imgur.com/DsjKP.png)