Final answer:
The question request cannot be fulfilled due to typeset or transcription errors in the provided function. For accurately finding a local maximum, the correct function form is required to differentiate with respect to 't' and apply mathematical tests.
Step-by-step explanation:
The question appears to contain typeset or transcription errors and does not provide a clear function to analyze for a local maximum with respect to the variable 't'. In the context of typical high school mathematics, we generally look for the value of 't' where the derivative of the function with respect to 't' is zero (indicating a potential maximum or minimum) and then analyze the second derivative or use other methods to distinguish if it's indeed a maximum.
To find a local maximum of a given function, we would normally differentiate the function with respect to 't', set the derivative equal to zero, and solve for 't'. However, without a correct form of the function, we can't perform these calculations.
If provided with a correct version of the function, we could proceed with finding the derivative with respect to 't', determining where this derivative equals to zero, and concluding whether these points correspond to local maxima by using the second derivative test or another suitable method.