Increasing function

Daniel123 · 2008-02-06 05:24:38

Just quickly..

By 'increasing function' do we mean a function with a positive slope as x increases positively or a function with an increasing gradient?

LuisRodg · 2008-02-06 05:53:47

An increasing function is one such that for every x and y: f(x) <= f(y) whenever x < y and "strictly" increasing f(x) < f(y) whenever x < y.

Last edited by LuisRodg (2008-02-06 05:57:40)

mathsyperson · 2008-02-06 05:57:02

Another way of thinking about it is that f(x) is increasing if f'(x) is always ≥ 0 (and strictly increasing if it's > 0).

LuisRodg · 2008-02-06 06:00:27

mathsyperson wrote:

Another way of thinking about it is that f(x) is increasing if f'(x) is always ≥ 0 (and strictly increasing if it's > 0).

Thats the best way to express it since its simpler and easier to understand. I just gave him the definition given to me in Discrete Math.

Daniel123 · 2008-02-06 06:02:12

In other words the gradient is positive?

mathsyperson · 2008-02-06 06:03:25

Yes, your description is the proper definition of "increasing", and mine's just how people generally think about it.

It's probably done that way because increasing functions are often defined before differentiation is taught.

LuisRodg · 2008-02-06 06:12:10

Daniel123 wrote:

In other words the gradient is positive?

Yes. The derivative f'(x) refers to the gradient or slope of the function. Therefore, like mathsyperson said if the function f has f'(x) >= 0 for every value of x then the function is increasing, if f has f'(x) > 0 for every x then it is "strictly" increasing.

Last edited by LuisRodg (2008-02-06 06:12:33)

Daniel123 · 2008-02-06 06:59:20

Right ok.. glad I got that straight. thanks.

TheDude · 2008-02-06 07:56:39

Daniel123 wrote:

In other words the gradient is positive?

Technically, that is sufficient but not necessary for a function to be increasing, since not all increasing functions are differentiable. However, if the function is differentiable and its gradient is positive you can be sure that it is increasing.

Daniel123 · 2008-02-06 08:02:57

Well seeing as this is in the chapter entitled "differentiation" I think I'm alright . Thanks.

Math Is Fun Forum

#1 2008-02-06 05:24:38

Increasing function

#2 2008-02-06 05:53:47

Re: Increasing function

#3 2008-02-06 05:57:02

Re: Increasing function

#4 2008-02-06 06:00:27

Re: Increasing function

#5 2008-02-06 06:02:12

Re: Increasing function

#6 2008-02-06 06:03:25

Re: Increasing function

#7 2008-02-06 06:12:10

Re: Increasing function

#8 2008-02-06 06:59:20

Re: Increasing function

#9 2008-02-06 07:56:39

Re: Increasing function

#10 2008-02-06 08:02:57

Re: Increasing function

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