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

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

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=(x-1)(x-2)^(2) .

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=(4x^(2)+1)/(x).

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=x^(2)+2x-5

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=x^(8)+6x^(2) .

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=(x+1)^(3)(x-3)^(3).

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=20-9x+6x^(2)-x^(3)

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=x^(3)-6x^(2)+9x+8

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=2x^(3)-15x^(2)+36x+17.

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=2x^(3)-9x^(2)+12x+15