Prove that the following functions are strictly increasing: `f(x)=log(1+x)-(2x)/(2+x)`

Prove that the following functions are strictly increasing: f(x)=cot^(-1)x+x

Prove that the function f(x)=x^(2)-2x-3 is strictly increasing in (2, infty)

Which of the following function is non-differentiable in domain? f(x)=(x-2)/(x^2+3) (b) f(x)=log|x| f(x)=x^3logx (d) f(x)=(x-3)^(3/5)

Find the intervals in which the functions are strictly increasing or decreasing: 10-6x-2x^(x)

Find the intervals in which the functions are strictly increasing or decreasing: -2x^(3)-9x^(2) -12x+1

Find the intervals in which the functions are strictly increasing or decreasing: x^(2) +2x-5

Find the intervals in which the functions are strictly increasing or decreasing: 6-9x-x^(2)

Find the intervals in which the functions are strictly increasing or decreasing: (x+1)^(3) (x-3)^(3)

Identify the following functions whether odd or even or neither: f(x)=log((x^4+x^2+1)/(x^2+x+1))

Prove that the function f(x)=x^(2)+2 is strictly increasing in the interval (2,7) and strictly decreasing in the interval (-2, 0).