Let the function f be defined by f(x)=xlnx, for all x>0. Then
Let f be a function defined on [a, b] such that f'(x) > 0, for all xϵ [a, b]. Then prove that f is an increasing function on [a, b].
Let f:(0,∞)→R be a differentiable function such that f′(x)=2−f(x)x for all xϵ(0,∞) and f(1)≠1. Then