Explore BrainMass
Share

Explore BrainMass

  1. Mathematics
  2. Calculus and Analysis
  3. 25686

Directional derivatives

Consider the function :
f(x,y) = x(x-1)(x-2) + (y-1)(x-y)

[QUESTION 1]find the maximum and the minim values of the
directional derivative (df/ds)]u at ( 1 , 3/2 ) as u varies .

( (df/fs)]u : I can't write the symbol clearly but it means : the derivative of f according to s on the direction of u (u is a unit vector).

[QUESTION 2] In which direction(s) "u", the maximum and the minimum occur?.

[QUESTION 3] What are the directions "u" for which (df/ds)u]=0

Solution Preview

In x direction, df/dx=(x-1)(x-2)+x(x-2)+x(x-1)+(y-1)
In y direction, df/dy=(x-y)-(y-1)
at the point (1,3/2) ...

Solution Summary

This shows how to find maximum and minimum values of the directional derivative.

$2.19

Related BrainMass Content

Directional Derivative

... Directional derivatives and gradients are investigated. Find the directional derivative
of the function at a given point P in the direction of the vector v The ...

Directional derivative

... Directional derivatives are determined. f (x, y, z ) = ex+y+3z The directional
derivative of a function f (x, y, z ) in the direction of the vector ⃗ is v. ...

direction derivative

Directional derivative. Let f(x) = e^(x+y+3z. a.) Find the directional
derivative at P(-2,2,-1) in the direction of Q(18,-2,4). ...

Multiple Variable Calculus

... Question 3. (a) Find the directional derivative of the function f(x, y) =
x2ey at the point (1,0) in the direction i + 2j. (b) Find ...

Derivatives : Velocity and Displacement

... to t is the speed; and the second derivative of H(t ... Note: the minus sign means the
direction of speed is ... Derivatives are applied to velocity and displacement. ...

Force and Direction on a Particle

... (b). at Point B the derivative is positive (the potential energy increases), hence
the force in negative and points in the negative x-axis direction. (c). ...

Gradient and divergence formulas

... the  -direction is (4) and the unit vector along the  -direction is (5 ... From
equations (3), (4), (5), we find the following partial derivatives (8) The ...

Electrostatics problems

... a particle experiences is minus the derivative wrt its ... minus the force exerted in
the positive r_1 direction. To calculate the derivatives it is convenient to ...