Maximizing an Exponential Function

Consider the function $$f(x) = 2^{x^2 - 4} + 3^{x - 1}$$. What is the value of $$x$$ for which $$f(x)$$ is maximized?

To find the maximum value of the function, you may want to explore its critical points by taking the derivative and setting it to zero. Analyze the behavior of this function at various points to determine where the maximum lies.