Question

(14) Find the maximum rate of change of f(x, y) = sin(xy) at the point (1, 0) and the direction in which it occurs.

Answer #1

Find the maximum rate of change of f at the given point
and the direction in which it occurs.
f(x, y) = 2 sin(xy), (0,
5)
direction of maximum rate of change (in unit vector) =
maximum rate of change =

Find the maximum rate of change of f at the given point
and the direction in which it occurs.
f(x, y) =
9 sin(xy), (0, 5)

Find the maximum rate of change of f at the given point
and the direction in which it occurs.
f(x, y) =
7 sin(xy), (0, 7)

Find the maximum rate of change and the direction in which it
occurs, to f(xy)=ln(x^2+y^2), at point (1,2).

let
f(x,y) = xe^(xy)
Find the directional derivative of f at point (2,0) in the
direction of vector <-6,8>. Find the maximum rate of change
of f at point (2,0) and the direction in which it occurs.

Let f (x, y) =
xe xy. Find the maximum rate
of change of f at the point (3, -2).

Find the directional derivative of the function
f(x,y)=x^6+y^3/(x+y+6 ) at the point (2,-2) in the direction of the
vector < - 2 ,2>.
b) Also find the maximum rate of change of f at the given
point and the unit vector of the direction in which the maximum
occurs.

let
f(x,y) = 2xy+4y^2
a) find the rate of change f at the point P(3,2) in the
direction of u= [1,3]
b) in what direction does f have the maximum rate of change?
what is the maximum rate id change?

1. Let f(x, y) = 2x + xy^2 , x, y ∈ R.
(a) Find the directional derivative Duf of f at the point (1, 2)
in the direction of the vector →v = 3→i + 4→j .
(b) Find the maximum directional derivative of f and a unit
vector corresponding to the maximum directional derivative at the
point (1, 2).
(c) Find the minimum directional derivative and a unit vector in
the direction of maximal decrease at the point...

a) evaluate the directional derivative of z=F(x,y) = sin(xy) in
the direction of u=(1,-1) at the point (0,pi/2)
b) Determine the slope of the tangent line
c) State the tangent vector

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