Please help me find the derivative and critical numbers for the following function. With steps Please!

f(x) = ((x^(-2)).(lnx))

f(x) = x^(-2) (ln x)

max, min or saddle point when

df/dx = 0

df/dx = (1 - 2 ln (x))/x^3 = 0

1 - 2 ln x = 0

x = √e

y = x^(-2) (ln x)

y = (√e)^(-2) (ln (√e))

y = 1/(2e)






inflection point when,

d²f/dx² = 0

d²f/dx² = (6 ln (x) - 5)/x^4 = 0

6 ln (x) - 5 = 0

x = e^(5/6)

y = x^(-2) (ln x)

y = (e^(5/6))^(-2) (ln (e^(5/6)))

y = 5/(6 e^(5/3))