Question: Consider the following functions f, points P, and unit vectors u. a. Compute the gradient of f and evaluate it at P. b. Find the

Consider the following functions f, points P, and unit vectors u.


f(x, y, z) = ln (1 + x + y + z);


a. Compute the gradient of f and evaluate it at P.


b. Find the unit vector in the direction of maximum increase of f at P.


c. Find the rate of change of the function in the direction of maximum increase at P.


d. Find the directional derivative at P in the direction of the given vector.

f(x, y, z) = ln (1 + x + y + z); P(1, 1, -1); 22 3'3' 3

Step by Step Solution

★★★★★

3.45 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a To compute the gradient of the function fx y z ln1 x2 y2 z2 we need to calculate the partial deriv... View full answer

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 Precalculus 1st Questions!

Q:

Consider the following functions f, points P, and unit vectors u. a. Compute the gradient of f and evaluate it at P. b. Find the unit vector in the direction of maximum increase of f at P. c. Find...

Q:

Consider the following functions f, points P, and unit vectors u.a. Compute the gradient of f and evaluate it at P.b. Find the unit vector in the direction of maximum increase of f at P.c. Find the...

Q:

Consider the following functions f, points P, and unit vectors u. a. Compute the gradient of f and evaluate it at P. b. Find the unit vector in the direction of maximum increase of f at P. c. Find...

Q:

Consider the following functions f, points P, and unit vectors u. a. Compute the gradient of f and evaluate it at P. b. Find the unit vector in the direction of maximum increase of f at P. c. Find...

Q:

Consider the following functions f, points P, and unit vectors u. a. Compute the gradient of f and evaluate it at P. b. Find the unit vector in the direction of maximum increase of f at P. c. Find...

Q:

Consider the following functions f, points P, and unit vectors u. a. Compute the gradient of f and evaluate it at P. b. Find the unit vector in the direction of maximum increase of f at P. c. Find...

Q:

Please help solve Consider the following function f, point P, and unit vector u. a. Compute the gradient of f and evaluate it at P. b. Find the unit vector in the direction of maximum increase of f...

Q:

Consider the following function f, point P, and unit vector u. a. Compute the gradient of f and evaluate it at P. b. Find the unit vector in the direction of maximum increase of fat P. c. Find the...

Q:

1. Consider the following function f, point P, and unit vector u. a. Compute the gradient off and evaluate it'at P. b. Find the unit vector in the direction of maximum increase offat P. c. Find the...

Q:

Consider the function f(x,y,z) = xyz-1, the point P(0, -3, -3), and the unit vector u = a. Compute the gradient of f and evaluate it at P. b. Find the unit vector in the direction of maximum increase...

Q:

An economic stimulus is an effort by the government to pump money into an ailing economy. Having studied the material presented in this chapter as well as in the last two chapters, discuss the effect...

Q:

A company has common stock and cumulative preferred stock. The preferred stock is 4%, $10 par, and there are 25,000 shares outstanding. The company didn't pay dividends in the previous two years. In...

Q:

Evaluate this statement: The current structure of the American Social Security system results in an intergenerational transfer of income and wealth.

Q:

=+2. What is the utility of positive psychology in promoting health for specific groups of children and adolescents (e.g., children with chronic illness, adolescents from disadvantaged backgrounds)?

Q:

For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as x approaches 0. i(x) = (1 + x) 4/x

Q:

For the following polynomial functions, find the derivatives. f(x) = 7x 2

Q:

For the following exercises, use technology to evaluate the limit. sin(x) lim x - 0 3x

Q:

On August 1. Pharoah Company buys 1,000 shares of Estrada common stock for $33,000 cash. On December 1, Pharoah sells the stock investments for $36,000 in cash. Journalize the purchase and sale of...

Q:

Review the Budget Comparison Statement for the Food Service Department in a Long Term Care Home. 1. For each cost center variance state if the variance has a positive or negative impact on the budget...

Q:

73. Inventory Costing MethodsPeriodic Method The Caitlin Company, which uses the periodic in ventory system, has the following records: Units Unit Cost Beginning inventory Purchases: Jan. 6 July 15...