Given,
f(x,y,z)=x−y2−z2 Now, level curve is defined as
Gf={(x,y,z)∈R3∣f(x,y,z)=c} That is, here, f−1(c)=Gf
Now, set
f(x,y,z)=c⟹(x−c)=y2+z2 Clearly, the level curves are family of paraboloid which passes through the center (c,0,0)
Here, blue, green and red are level curve of f−1(−1),f−1(0)&f−1(1) respectively.
Comments