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I know to find inflection points I have to:

1. Compute f''(x)

2. Determine the points in the domain of f for which f''(x) = 0 or f''(x)

does not exist

3. Determine the sign of f''(x) to the left and right of each point x = c

found in step 2. If there is a change in the sign of f''(x) as we move

across the point x = c, then (c, f(c)) is an inflection point of f.

Well, this is what I came up with:

f'(x) = e^x -x^-2

f''(x)= e^x + 2x^-3

Then, I don't know what to do from there because e^x can never be zero, right? but I don't know. My teacher is saying there are inflection points...

Your help is much appreciated!

Sam