differentiation

Aug 2009
639
2
given that f(x,y) =(x^3 +y^3) ^(1/3). determine whether fy(0,0) exist?


my working:

i differentiated wrt to y, and then sub in (0,0) and i got that fy=0.

but my answer says that fy exists...
 
Apr 2010
384
153
Canada
given that f(x,y) =(x^3 +y^3) ^(1/3). determine whether fy(0,0) exist?


my working:

i differentiated wrt to y, and then sub in (0,0) and i got that fy=0.

but my answer says that fy exists...
If a derivative exists what does that mean? Can a derivative exist and have a value of 0?

Well, what is a derivative? A derivative will tell us the slope of the tangent to the curve at a given point. Let me ask you this, can we have a horizontal tangent to the curve (i.e. no slope) and if we can, does this still "exist"?