need help on this business cal problem

[tinyT12]

f(x)=x-4/x^2 and i have to find all the values of x that correspond to horizontal tangent lines and select none if the function does not have any values of that correspond?

 

[BigGlenntheHeavy]

\(\displaystyle f(x) \ = \ x-\frac{4}{x^{2}}, \ f'(x) \ = \ 1+\frac{8}{x^{3}} \ = \ 0 \ \implies \ x \ = \ -2\)

\(\displaystyle f(-2) \ = \ -3, \ f'(-2) \ = \ 0 \ = \ m, \ hence \ y \ = \ -3 \ (horizontal \ tangent), \ see \ graph.\)

[attachment=0:3sz4d4pb]def.jpg[/attachment:3sz4d4pb]