Finding turning point, rel. minimum or max., and point of inflection....?

Question

Find turning point, rel. minimum or max., and point of inflection for:

f(x)=x^2-4/x

and

g(x)=1/3x^3-x^2+x-3

Thanks in advance!

Answer 1

f´(x) = 2x+4/x^2 = (8x^3+4)/x^2 = 0 so x= (-1/2)^1/3 local minimum
f´´(x) = 2-8/x^3 = 0 //2x^3-8=0 // x=(4)^1/3 inflection point
g´(x) = x^2-2x+1 =0 //x=1 (double root) no max nor min)
g´´(x) 2x-2=0 //x=1 //inflection point