What is the minimum value of the sum of a positive real number and its reciprocal?

Question

Question: What is the minimum value of the sum of a positive real number and its reciprocal?


And please explain. x_x;; Thank you in advance!

Answer 1

You're trying to minimize f(x) = x + 1/x.

If you're in a calculus class, take the derivative f' and set it equal to 0. There will be one positive value of x where the derivative is zero, and it will indeed give a minimum for the function.