prove that E(ax+b)=aE(x)+b where a and b are constants

Prove that f(x) = ax + b, where 'a and b' are constants and a> 0 is a strictly increasing function for all real values of x, without using the derivative.

Prove that f(x)=a x+b , where a , b are constants and a >0 is an increasing function on Rdot

Prove that f(x)=a x+b , where a ,\ b are constants and a >0 is an increasing function on R .

Prove that f(x)=a x+b , where a ,\ b are constants and a<0 is a decreasing function on R .

A function is defined as f(x) = ax^(2) – b|x| where a and b are constants then at x = 0 we will have a maxima of f(x) if

Prove that f(x)=ax+b, where a,b are constants and a>0 is an increasing function on R.

Prove that f(x)=ax+b, where a,b are constants and a>0 is an increasing function on R.

Prove that f(x)=ax+b, where a,b are constants and a<0 is a decreasing function on R.

Let f(x) =ax^(2) -b|x| , where a and b are constants. Then at x = 0, f (x) is