Show that the curve... (1 Viewer)

[matreha]

Hi everyone,

I have a maths question:

Show that the curve y = 2x^3 + 6x -2 is always increasing.

I have no idea how to do this!

Thanks!

 

[matreha]

Please help!

 

[funnytomato]

Please help!

Have you made any progress so far?

If yes, please let us know what you have and specify which part you're having trouble with?

If not, have you learned differentiation yet?

 

[funnytomato]

What is the derivative of y = 2x^3 + 6x -2 ?

if you've found the derivative, what does it mean for a function to be increasing ? (in terms of its derivative y' )

and note for any n(positive or negative or 0), we always have n^2 >= 0

 

[matreha]

What is the derivative of y = 2x^3 + 6x -2 ?

if you've found the derivative, what does it mean for a function to be increasing ? (in terms of its derivative y' )

and note for any n(positive or negative or 0), we always have n^2 >= 0

Thanks for your help! I found the derivative to be y' = 6x^2 + 6
and I know that y'>0 so 6x^2+6>0

I'm not sure where to go from there...

 

[Kaido]

If the derivative is >0 then the function is increasing (derivative = gradient)

 

[funnytomato]

Thanks for your help! I found the derivative to be y' = 6x^2 + 6
and I know that y'>0 so 6x^2+6>0

I'm not sure where to go from there...

The reasoning should actually go the other way around, if you know what I mean

"The function y = 2x^3 + 6x -2 is always increasing" means that you have to show (as Kaido said)
"y'>0 for all x values" in the domain of the function (in this case it's just all real x)

You found the derivative to be

And you need to show is always positive for all in the domain

Note for ,

, hence we have



i.e We just showed that y'>0 for all real x , therefore the function y is always increasing