a) On what interval is f(x) = xlnx decreasing?

b) On what interval is f concave upward?

My attempt:

a) f'(x) = (x)d/dx(lnx) + (lnx)d/x(x)

= x * 1 / x + lnx

= lnx

According to lnx graph, f(x) decreasing when 0 < x < 1

b) f''(x) = 1 / x

According to 1 / x graph f concave upward when x < 0