What are the critical values, if any, of f(x)= x^2*(1 + 3 ln x)?

1 Answer
Sep 7, 2017

To find critical values, we just have to set f'(x) = 0

Explanation:

f(x) = x^2*(1 + 3 ln x)

implies f'(x) = 2x*(1+3lnx) + (x^2) * (3/x)
implies f'(x) = 2x*(1+3lnx) + 3x
implies f'(x) = 0
implies 2x*(1+3lnx) + 3x =0
implies x(2*(1+3lnx) + 3) = 0
implies x = 0 or (2*(1+3lnx) + 3)=0
implies x=0 or x=e^(-5/6)