How do you find the local max and min for f(x)=x+(1/x)?

1 Answer
Mar 6, 2017

Local f_min= (1, 2)
Local f_max = (-1, -2)

Explanation:

f(x) =x+1/x

f(x) will have extrema where f'(x)=0

f'(x) = 1-1/x^2 [Power rule]

1-1/x^2 =0 -> x^2=1

x= +-1

As can be seen by the graph of f(x) below, f(x) has a local maximum at x=-1 and a local minimum at x=+1

graph{x+1/x [-12.66, 12.65, -6.33, 6.33]}

Therefore:
Local f_min = f(1) = 1+1 =2 -> (1,2)
and
Local f_max = f(-1) = -1-1 =-2-> (-1,-2)