Let f(x)=2/[1+(e^(-x))], x=all real #'s (a) Determine where f(x) is increasing and where it is decreasing. (b) Where is the function concave up and

Let f(x)=2/[1+(e^(-x))], x=all real #'s(a) Determine where f(x) is increasing and where it is decreasing.(b) Where is the function concave up and where is it concave down? Find all inflection points of f(x).(c)Find lim x-->infinity f(x) and decide whether f(x) has a horizontal asymptote.(d)Find lim x-->infinity f(x) and decide whether f(x) has a horizontal asymptote.(e)Sketch the graph of f(x) together with its asymptotes and inflection points (if they exist).