What is the second derivative of x2 ln x?

Answer 1

First one:

f'(x) = 2x*lnx + x^2*(1/x) = 2x*lnx + x = x*(2*lnx + 1)

Second derivate:

f"(x) = D [x*(2*lnx + 1)] = 1*(2*lnx + 1) + x*(2/x)

= 2*lnx+1+2

= 2*lnx + 3

So, there is a minimum in this graph on point (1/e^(1/2)), -1/(2e)) = MIN(x, y)

Van Sanden David

Belgium