I am trying to work out the range of f(x) = x + 1/x, after sketching it, i notice i can use calculus to find the turning points

and establish it that way:x plus i over x.jpg

But are there methods i can use that do not involve calculus? I am working with my son who hasn't met Calculus so i am trying to establish alternative approaches. I thought about guessing values and trying either side but that feels like you already know what the answer is? Unless someone can convince me this method is ok to do.

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