T/F and why(true/false)?
(Part a) If the partial derivatives fx(x,y),
fy(x,y) exists for all values x,y ,then f(x,y) is
continuous.
(Part b) Suppose f(x,y) is a function which is differentiable
and nonnegative everywhere, and is zero at the origin
,f(x,y) ≥ 0, f(0,0) = 0.Then the gradient vector is zero at the
origin is,∇f(0,0) = (0,0).
(Part c) If F(x,y) is continuous on the entire plane, then there
is a function f:R→R satisfying
f′(x) =F(x,f(x)), f(0) = 0 for all...