Question: Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. f(x,y,z)

Find the directions in which the function increases and decreases most

Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. f(x,y,z) = (x/y) - yz, Po(4, - 1, - 3) The direction in which the given function f(x,y,z) = (x/y) - yz increases most rapidly at Po (4, - 1, - 3) is u = + (Type exact answers, using radicals as needed.)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. f( x, y,z) = (x/y)-yz, Po(- 1, - 1, -4) The...

a Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. f(x,y,z) = (x/y) -yz. Po(-4, - 1,1) The...

Find the directions in which the function increases and decreases most rapidly at Po Then find the derivatives of the function in these directions f x y z x y yz Po 1 1 4 5 27 j The direction in...

Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. f(x,y,z) = (x/y) -yz, Po(- 4, - 1, - 1) The...

1 Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. f(x,y,z) = (x/y) - yz, Po(-3,1, - 1)Solve by the...

Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in those directions. f(x,y,z) = In (xy) + 3 In (yz) + 2 In (xz), Po(1,...

1 Solve the initial value problem for r as a vector function of t. dr Differential equation: dt = -7ti- 7t j - 3t k Initial condition: r(0) = 5i + j + 9k r(t) = it + kFind the derivative of the...

\fFind the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. f(x,y, z) = (x/y)-yz, Po(2, 1, - 3) . . . The...

1 Find the gradient of the function g(x,y) = xy at the point (1, - 2). Then sketch the gradient together with the level curve that passes through the point. First find the gradient vector at (1, -...

question below: Find the directions in which the function increases and decreases most rapidly at P0. Then nd the derivatives of the function in these directions. le.y.Z)= (xly) -yz, Po(2, - 1, - 1)...

Consider the following two groups of words: Group 1 Group 2 AREA...................ERST FORT...................FOOT HOPE...................HEAT SPAR...................PAST THAT...................PROF...

Do you think Wal-Mart and the other large retailers are going too far in their demands on their suppliers? Where would you draw the line?

How dynamic is the industry in which your company is based? Is there any evidence that innovation is reshaping competition or has done so in the recent past?

The force constant of a massless spring is 2 5 . 0 N / m . A mass of 0 . 4 5 kg is oscillating in simple harmonic motion at the end of the spring

Can algorithms understand and interpret patterns of activities to predict behavior and preferences?

Managers engage in strategic planning for their organizations but will also have tactical measures as an extension of these strategies. Environmental conditions can and will change, and so should...

Would algorithms hamper learning. How could organizations support learning and innovation?