Determine whether the statement is true or false. Explain your answer. In each exercise, assume that f denotes a differentiable function of two variables whose domain is the x y -plane . If v = 2 u then the directional derivative of f in the direction of v at a point x 0 , y 0 is twice the directional derivative of f in the direction of u at the point x 0 , y 0 .
Determine whether the statement is true or false. Explain your answer. In each exercise, assume that f denotes a differentiable function of two variables whose domain is the x y -plane . If v = 2 u then the directional derivative of f in the direction of v at a point x 0 , y 0 is twice the directional derivative of f in the direction of u at the point x 0 , y 0 .
Determine whether the statement is true or false. Explain your answer. In each exercise, assume that
f
denotes a differentiable function of two variables whose domain is the
x
y
-plane
.
If
v
=
2
u
then the directional derivative of
f
in the direction of
v
at a point
x
0
,
y
0
is twice the directional derivative of
f
in the direction of u at the point
x
0
,
y
0
.
Determine the set of points (x, y) ∈ R2 where we have y as a function of x according to the equation in the image. What happens and why does it happen?
Explain how to approximate the change in a function ƒ when the independent variables change from (a, b) to (a + ∇x, b + ∇y).
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