For the function `f(x)=(e^x)/(1+e^x),` which of the following hold good? `f` is monotonic in its entire domain. Maximum of `f` is not attained even though `f` is bounded `f` has a point of inflection. `f` has one asymptote.

For the function y=f(x)=(x^2+bx+c)e^x , which of the following holds ?

Domain of the function f (x)= (x)/(log _(e) (1+x)) is-

Consider the function f:(-oo,oo)to(-oo,oo) defined by f(x)=(x^2-a)/(x^2+a),a >0, which of the following is not true?(a) maximum value of f is not attained even though f is bounded. (b) f(x) is increasing on (0,oo) and has minimum at x=0 (c) f(x) is decreasing on (-oo,0) and has minimum at x=0. (d) f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

f(x)=e^x-e^(-x) then find f'(x)

Draw the graph of f(x) = e^(x)/(1+e^(x)) . Also find the point of inflection.

If f(x)=x.e^(x(1-x)) , then f(x) is

If the function f(x)=x^(3)+e^((x)/(2)) and g(x)=f^(-1)(x) , then the value of g'(1) is

Let f(x)=(x)/(1+|x|) Domain of f(x) is-

For the cubic function f(x)=2x^3+9x^2+12 x+1, which one of the following statement/statements hold good? 1 . f(x) is non-monotonic. 2 . f(x) increases in (-oo,-2)uu(-1,oo) and decreases in (-2,-1) 3 . f: RvecR is bijective. 4 . Inflection point occurs at x=-3/2dot

Show that the function given by f(x) = (logx)/(x) has maximum at x = e.