algebra
Algebra
Level
2
X is a negative real number , what is the maximum value of x +1/x ?
The answer is -2.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The derivative of x+1/x is 1-1/x^2. When 1-1/x^2=0, x= -1 or 1. These are the critical numbers. One is the x-value for the minimum and the other is the x-value for the maximum. Since x is supposed to be a negative real number, that means that x= -1 is the value to use. If one plugs back in to the original equation: (-1)+1/(-1)= -1-1= -2. The maximum value for this equation with a negative number for x is -2.