f(x) = x + 1/x

f(x) = x + x^-1

f'(x) = 1 - x^-2

f'(x) = 1 -1/x^2

f"(x) = 2x^-3

f"(x) = 2/x^3

To find critical point value of x, I set f'(x) = 0 and solve for x

To find inflection point value of x, I set f"(x) = 0 and solve for x.

Unfortunately, this problem doesn't make solving for x very easy.