What is the difference between strictly increasing and increasing functions?I came across this topic on chapter "Application of Differentiation "

Question

aravindg · Answer

The definition in my text seems absurd ...Well how do we find if given function is strictly increasing or simply increasing ?

compassionate · Answer

Strictly increasing functions...STRICTLY increase. Lots of rules and regulations. Gosh. They can be so strict sometimes!

experimentx · Answer

a non decreasing = increasing
strictly increasing ... must increase with increase in your independent variable.

experimentx · Answer

$$y > x, f(y) \ge f(x) \text{ (increasing)} \
y > x, f(y) > f(x) \text{ ( strictly increasing)} $$

anonymous · Answer

As for how to find whether a function is increasing/decreasing, you can apply the first derivative test, which will tell you over which intervals a given function is increasing/decreasing, depending on the sign of the derivative over each interval.

aravindg · Answer

@SithsAndGiggles what do i do to find whether its strictly increasing or decreasing?

kropot72 · Answer

@AravindG I think that your answer is here: http://mathworld.wolfram.com/StrictlyIncreasingFunction.html

anonymous · Answer

@AravindG, are you familiar with the first derivative test?

aravindg · Answer

yes

shubhamsrg · Answer

strictly inc when f'(x) > 0
inc when f'(x) >= 0

aravindg · Answer

|dw:1363415541751:dw|

is this graph strictly increasing?

shubhamsrg · Answer

yes

aravindg · Answer

hw abt this 
|dw:1363415691004:dw|

shubhamsrg · Answer

http://www.youtube.com/watch?v=1mW6pOq7CsI

aravindg · Answer

well can u answer that ^^

aravindg · Answer

in ncert text they say it is example for  increasing

shubhamsrg · Answer

I'd say it is strictly inc but my inner voice says otherwise! :3

shubhamsrg · Answer

I might still go with strictly inc

shubhamsrg · Answer

I should*

aravindg · Answer

so is that a mistake ?

shubhamsrg · Answer

strictly inc func are inc func but inc func are not generally strictly inc.

aravindg · Answer

so what is a function ? :|

shubhamsrg · Answer

1 value of y for a particular x

aravindg · Answer

of course i knw dat

shubhamsrg · Answer

glad you know that! ^_^

aravindg · Answer

;)

aravindg · Answer

this is gonna be good :)

shubhamsrg · Answer

:D

shubhamsrg · Answer

reminds me of the most non pollutant means of transport! :')

aravindg · Answer

haha :D