Question

Application of Derivatives -

Problem

What is the difference between decreasing and non-increasing functions?

Answer 1

@ganeshie8

Answer 2

strictly decreasing : rate of change is always negative
decreasing : rate of change is always negative or 0

Answer 3

`non-increasing` may be referring to the `decreasing` functions

Answer 4

do u have definitions for these ?

Answer 5

yeah, that I understand.

Strictly Decreasing => f(x) is strictly decreasing in (a,b) iff f'(x) < 0 for all x belonging to (a,b) .

Decreasing => f(x) is a decreasing function in (a,b) iff f'(x) \(\le 0\) , may hold ONLY for discrete values of x i.e. \(f(x) \ne 0\) for any sub interval in (a,b)

Answer 6

While the course I am studying from, defines NON-increasing functions as

f(x) is said to be NOn-increasing in (a,b) iff \(x_1 < x_2\) \(\implies f(x_1) \ge f(x_2) \) for all, \(x_1 , x_2\) belonging to (a,b).

Answer 7

i was sketching something like that xD