define-increasing-and-decreasing-function-with-example-

Question Number 159338 by zakirullah last updated on 15/Nov/21

d e f i n e i n c r e a s i n g

a n d d e c r e a s i n g f u n c t i o n w i t h e x a m p l e ?

Answered by physicstutes last updated on 15/Nov/21

increasing function

Let f (x) be a function . Then

f (x) is an increasing function

if it has a positive gradient .

That is f^{'} (x) > 0 .

For example : f (x) = x^{3} + x

is always increasing . Why ?

f^{'} (x) = 3 x^{2} + 1 > 0 \forall x \in R .

decreasing function

Let g (x) be a function . Then g (x) is

called a decreasing function if it has

a negative gradient . That is g^{'} (x) < 0 .

For example :

g (x) = - x^{3} - x is always decreasing .

Why ?

g^{'} (x) = - (3 x^{2} + 1) < 0 \forall x \in R

Commented by zakirullah last updated on 16/Nov/21

v e r y w e l l s i r G