maths(p1)

[bibeksharma]

given that y=(x^3 +1)^(1/2), show that (dy/dx)>0 for all x>-1.

 

[Nikesh]

its so simple man!!!!!!!!!!!!!!!!!!!!!
firstly differentiate the given equation and then check the value of dy\dx with the values greater than -1.
You will get you answer right after it.....
got it or still confused!!!!!!!!!!!!

 

[Bimal]

look dari, first find dy/dx by using dy/dx=dy/du*du/dx where u=(x^3+1).then you will get dy/dx=(3x^2)/2(x^3+1)^-1/2 then
,for the function to be definable x^3+1>0
x>-1
put a value greater than -1 in dy/dx then you will get dy/dx>0.
Got itt.if not we will discuss in colg.

 

[Nikesh]

but the mind blowing fact is that the equation is satisfied by all the values of x except 0.
If we keep the value of x=0, dy/dx gives the value 0 which is not greater than 0 as the question says to prove it!!!!

 

[anzaar]

what about
If you plug in x=-1, the derivative does not exist(becomes undefined).
Bimal adopted right procedure.

 

[MAVtKnmJ]

I think you are forgetting that as per the question, x > -1 and not x = -1