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Answer 1 · 2017-12-03T06:22:45

That is correct. Furthermore, the function increases for #x>=1/2#

A function is increasing if #frac{dy}{dx} > 0#.

#frac{dy}{dx} > 0#
#8x - 1/x^2 >0#

Since #x^2 > 0#, multiplying it to both sides of the inequality retains the sign.

#8x^3 - 1 > 0#
#8x^3 > 1#
#x^3 > 1/8#

Since the cube root is an increasing function, taking the cube root on both sides does not change the sign too.

#x > 1/2#

The point #(1/2,3)# is included as well.