Question
In: Math
Find the maximum rate of change of f at the given point and the direction in...
Find the maximum rate of change of f at the given point and the direction in which it occurs.
f(p, q) = 3qe-p + 2pe-q, (0, 0)
direction of maximum rate of change (in unit vector)
Solutions
milcah answered 2 years agoRelated Solutions
Find the directional derivative of f at the given point in the direction indicated by the...
Find the directional derivative of f at the given point
in the direction indicated by the angle θ.
f(x, y) =
y
cos(xy), (0,
1), θ = π/4
Duf(0,
1) =
Find the directional derivative of f(x,y)=arctan(xy) at the point (-2,5) in the direction of maximum decrease.
Find the directional derivative of f(x,y)=arctan(xy) at the point (-2,5) in the direction of maximum decrease. What is the Domain and Range of f(x,y)=arctan(xy)?
A) Find the directional derivative of the function at the given point in the direction of...
A) Find the directional derivative of the function at the given
point in the direction of vector v. f(x, y) = 5 + 6x√y, (5, 4), v =
<8, -6>
Duf(5, 4) =
B) Find the directional derivative,
Duf, of the function at the given
point in the direction of vector v.
f(x, y)
=ln(x2+y2), (4, 5),
v = <-5, 4>
Duf(4, 5) =
C) Find the maximum rate of change of f at the given
point and the direction...
Find the directional derivative of the function at the given point in the direction of the...
Find the directional derivative of the function at the given
point in the direction of the vector v. ? = (2? + 3?)2, ? ⃑ = 1 2 ?
⃑+ √3 2 ? ⃑, (-1,1,1)
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) =...
Find the absolute maximum and absolute minimum values of
f on the given interval.
f(x) = x3 − 5x + 8, [0, 3]
absolute minimum value
absolute maximum value
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) =...
Find the absolute maximum and absolute minimum values of
f on the given interval.
f(x) = x3 − 6x2 + 9x +
4, [−1, 8]
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) =...
Find the absolute maximum and absolute minimum values of
f on the given interval.
f(x) = 4x3 −
6x2 − 144x +
5,
[−4, 5]
absolute minimum
absolute maximum
use Lagrange multipliers to find the maximum and minimum values of f subject to the given...
use Lagrange multipliers to find the maximum and minimum values
of f subject to the given constraint, if such values
exist. f(x, y, z) =
xyz, x2 + y2 +
4z2 = 12
Find the maximum and minimum values of f subject to the given constraints. Use a computer...
Find the maximum and minimum values of f subject to the
given constraints. Use a computer algebra system to solve the
system of equations that arises in using Lagrange multipliers. (If
your CAS finds only one solution, you may need to use additional
commands. Round your answer to four decimal places.)
f(x, y,
z) = yex
−
z; 9x2
+ 4y2 +
36z2 =
36, xy + yz = 1
Let f(x,y) = 3x^2 + 6xy a) find the rate of change of f at the...
Let
f(x,y) = 3x^2 + 6xy
a) find the rate of change of f at the point P(3,2) in the
direction of u = [3,4]
b) In what direction does f have the maximum rate of change?
what is the maximum rate of change?
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