Find the directions in which the function f (x, y, z) = sett + z2 increases and decreasesmost rapidly at the point P(1,1n 2,1/2)

Question

Find the directions in which the function f (x, y, z) = sett + z2 increases and decreasesmost rapidly at the point P(1,1n 2,1/2)
🧐 Not the exact question you are looking for?Go ask a question

Solution 1

The function given is f(x, y, z) = x + z^2. To find the directions in which the function increases and decreases most rapidly at the point P(1, 1, 2, 1/2), we need to find the gradient of the function.

The gradient of a function is a vector that points in the direction of the greatest rate of incre Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

This problem has been solved

Similar Questions

Find the directions in which the function f (x, y, z) = sett + z2 increases and decreasesmost rapidly at the point P(1,1n 2,1/2)

The notation of bivariate function is represented as*x=fa(x,y)z=fab(x,y)f=az(x,y)z=f(x,y)

If x2 + y2 + z2 = 9, dxdt = 4, and dydt = 8, find dzdt when (x, y, z) = (2, 2, 1).

Find the gradients of the following functions:(a) f (x, y, z) = x2 + y3 + z4 .(b) f (x, y, z) = x2 y3 z4 .(c) f (x, y, z) = e x sin(y) ln(z)

The Jacobian of p,q,r w.r.t x,y,z given p=x+y+z, q=y+z, r=z is ________Review Later021-2

1/3