Find a number x in the closed interval ....

Question

 Find a number x in the closed interval (2/3,4/3) such that the sum of the number and its reciprocal is:

a). as small as possible

b). as large as possible

Answer 1

Graph it! Then use the derivative.

x+(1/x) has an absolute minimum at x=1 and in the interval stated the maximum occurs when x=2/3