To find maxima for Gaussian mixture model I have a Gaussian mixture model with some parameters 
mean=(506.8644,672.8448,829.902)
sigma=(61.02859,9.149168,74.84682)
c=(0.1241933, 0.6329082, 0.2428986)
And the plot look something like below. 

Also, if I change my parameters to 
mean=(2.15,2.0,2.9)
sigma=(0.1,0.1,0.1)
c=(1/3,1/3,1/3)
Then plot would change to 

Is there any way to find the maxima. I have tried Newton's method but it gave me the wrong output.
Like in general some common solution, which would work on all the cases, is needed.Can someone suggest me how can I achieve this 
Thanks in advance
 A: As whuber mentioned below, the mode of the mixture may not be a mode of any component. 
This seems to be a fairly comprehensive overview of mode-seeking algorithms for GMMs. 
One technique is to run a local optimization algorithm centered on each mixture component. 
According to the document, when all the components have equal variance, which is not the case here, this algorithm will almost always succeed, barring pathological cases. When the components do not have equal variance, there are no such guarantees.
Another method is to set the gradient of the likelihood to 0 and use the mean-shift algorithm for mode seeking:
$$
x \leftarrow \frac{\sum_i f_i(x)\mu_i}{\sum_i f_i(x)}
$$
where $x$ can be initialized to any reasonable value (or perhaps even multiple) and $f_i$ is the density of the $i$th component at $x$, accounting for the mixture weights.
This algorithm performs decently, but also seems to have no global convergence guarantees.
Finally, the method proposed in the document suggests finding the mode of the gaussian distribution by relaxing the original density into a very smooth mixture which only has one maximum, and iteratively tightening the mixture until it returns to the original mixture.
More concretely, the convolution of a gaussian with another gaussian results in a gaussian. Therefore, we can analytically convolve a smoothing gaussian with an GMM, giving us another GMM. If we make the variance of the smoothing gaussian sufficiently large, we will end up with a unimodal density. 
At this point, we should maximize the likelihood, reduce the variance of the smoothing gaussian, and repeat. Do this until the variance reduces to 0, at which point we have found some mode of the original mixture. 
The document claims that this algorithm will find either the global maximum or a mode which is close to the global maximum, but doesn't provide any guarantees.
