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 .

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 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)=ax+b, where a,b are constants and a<0 is a decreasing function on R.

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

Prove that f(x)=ax+b is decreasing function,a,b= constants and a <0

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

Let f(x) = (x)/(sqrt(a^(2) + x^(2)))- (d-x)/(sqrt(b^(2) + (d-x)^(2))), x in R , where a, b and d are non-zero real constants. Then, (A) f is an increasing function of x (B) f' is not a continuous function of x (C) f is a decreasing function of x (D) f is neither increasing nor decreasing function of x

Prove that f (x) = e^(3x) is strictly increasing function on R.