fuzzybottom

two questions im stuck on, don't have access to the teacher atm so i can't ask until tomorrow.

graph of f`, derivative of f, has a domain of 0>x>2 and since i cant draw it
here: its a straight line from (0,0) to (1,1) then a straight line from (1,1)
to (2,0) and it exists at (1,1).
if it asks for an expression for f`(x), the graph they give, in terms of x,
do you guys think they want the set of equations with domain restrictions that would cause that, or what? i end up having to write the expression for f(x) after that given f(1) = 0, i can do that part, but i dont know what to
do about the first part.
if its the set of equations i've got:
f`(x) = x, 0 < x < 1
f`(x) = 1, x=1
f`(x) = 2-x, 1 < x < 2

and does anyone know about vertical tangent lines for x² + xy + y² = 27
im still not sure about questions like this, whether there is a vertical tangent line or what, since when i take the derivative i get
dy/dx = -(2x + y)/(x + 2y)
and for there to be a veritical tangent line that would have to be undefined at some point, so x must be -2y, and x=-2y has infinite solutions =/

thanks for any help you can give