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Obtaining the maximum by means of the second derivative criterion only ensures that they have a local

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Certain components of a system have an exponential duration with mean 0, that is (image). Find the EMV of 0 by derivation, study the likelihood function and check if it is a global maximum. Explain and include graphs. I tried to solve it by my own but it seems I failed to prove the estimate is a global maximum. Work in images The comments I got were: Obtaining the maximum by means of the second derivative criterion only ensures that they have a local but not a global maximum, to find the global maximum they must study the likelihood function (see how they behave at the extremes of theta values). They should also add the graph of the likelihood function to help them understand the behavior of the function. 

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