Find the Global Maximum and Minimum values of the function. The domain is all real numbers unless otherwise specified.

Question

Find the Global Maximum and Minimum values of the function. The domain is all real numbers unless otherwise specified.

 

f(x)=x+1/x  for x>0

Answer 1

f(x) = x + 1/x

 

This function has a discontinuity at x = 0.

 

lim_x->0+ x+1/x = +∞

 

There is no absolute/global maximum value.

 

f'(x) = 1 - 1/x²

f'(x) = 0 when x = ±1. We ignore negatives, so x=1.

 

f''(x) = 1/x³

f is concave up for all positive x. Therefore, x=1 is a minimum.

 

f(1) = 1 + 1/1 = 2 is the minimum value for x>0.