a) On what interval is f(x) = xlnx decreasing?
b) On what interval is f concave upward?
a) f'(x) = (x)d/dx(lnx) + (lnx)d/x(x)
= x * 1 / x + 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