Any function f(x) is an increasing function in [a, b] if :

(A) $\forall ~x_1, x_2 \in[a, b], f\left(x_1\right) ≥ f\left(x_2\right)$ if $x_1<x_2$
(B) $\forall ~x_1, x_2 \in[a, b], f\left(x_1\right) ≥ f\left(x_2\right)$ if $x_1>x_2$
(C) $\forall ~x_1, x_2 \in[a, b], f\left(x_1\right) ≤ f\left(x_2\right)$ if $x_1<x_2$
(D) $\forall ~x_1, x_2 \in[a, b], f\left(x_1\right) < f\left(x_2\right)$ if $x_1>x_2$

Choose the correct answer from the options given below :

(B), (C) Only

f(x) increasing in [a, b]

if for $\forall ~x_1, x_2 \in[a, b]$

$f(x_1) ≥ f(x_2)$  if  $x_1 > x_2$

OR

$f(x_1) ≤ f(x_2)$  if  $x_1 < x_2$

if value of y > x

then f(y) > x to be increasing in subsequent values