Question: Find the directions in which the functions increase and decrease most rapidly at P 0 . Then find the derivatives of the functions in these

Find the directions in which the functions increase and decrease most rapidly at P0. Then find the derivatives of the functions in these directions.

h(x, y, z) = ln (x2 + y2 - 1) + y + 6z, P0(1, 1, 0)

Step by Step Solution

★★★★★

3.47 Rating (173 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To find the directions of the fastest increase and decrease of the function we need to find the grad... 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 Questions!

Q:

In Exercises find an equation of the line that is tangent to the graph of and parallel to the given line. Function f(x) = x Line 3x = y + 1 = 0

Q:

Predict the product of each of the following Diels-Alder reactions for the diene (left) and dienophile (right) as shown below. 0 0 0 0

Q:

Find the directions in which the functions increase and decrease most rapidly at P 0 . Then find the derivatives of the functions in these directions. (x, y, z) = ln xy + ln yz + ln xz, P 0 (1, 1, 1)

Q:

Find the directions in which the functions increase and decrease most rapidly at P 0 . Then find the derivatives of the functions in these directions. (x, y) = x 2 y + e xy sin y, P 0 (1, 0)

Q:

Find the directions in which the functions increase and decrease most rapidly at P 0 . Then find the derivatives of the functions in these directions. g(x, y, z) = xe y + z 2 , P 0 (1, ln 2, 1/2)

Q:

Find the directions in which the functions increase and decrease most rapidly at P 0 . Then find the derivatives of the functions in these directions. (x, y, z) = (x/y) - yz, P 0 (4, 1, 1)

Q:

Find the directions in which the functions increase and decrease most rapidly at P 0 . Then find the derivatives of the functions in these directions. (x, y) = x 2 + xy + y 2 , P 0 (-1, 1)

Q:

Please show all your work and highlight answer. thank you Problem 1: (Gradient vector) Given f (x, y) = x2 + y2, find Vf. Graph some level curves and vectors Vf at the following points: P1 (1,1), P2...

Q:

Calculus 3 Section 14.5 Reading Assignment: Directional Derivatives and Gradient Vectors I am suck with this question. Please help! Section 14.5 Reading Assignment: Directional Derivatives and...

Q:

Section 14.5: Problem 5 ('I point) Find the directions in which f increases and decreases most rapidly at point P. Then find the derivatives of f in these directions. f(w, y) : 3mg + 5mg + 73,2, P :...

Q:

What is meant by the term bribery?

Q:

Assume that you had speculated the day of DC1 by purchasing put options that specify 1 million units of the foreign currency. You then disposed of your contracts the day of DC2 or exercised them if...

Q:

On June 1, the unpaid balance in an account was $193. On June 11, a payment of $20 was made. The interest rate per month was 1.5% per month of the average daily balance. Find the new balance at the...

Q:

66. Suppose the time spent by a randomly selected student who uses a terminal connected to a local time-sharing computer facility has a gamma distribution with mean 20 min and variance 80 min2 . a....

Q:

Use substitution and partial fractions to find the indefinite integral. 1 x(3-x) - dx

Q:

Use a table of integrals to find the indefinite integral. er (1-ex)/20 dx

Q:

Use a table of integrals to find the indefinite integral. 1 x2 + 9x dx

Q:

The accounting principle that guides accountants, when faced with a recognition dilemma, to choose the alternative that produces the lowest net income is referred to as: the matching concept....

Q:

heridan AME ENGAGE English (en) rrect out of Take me to the text Feng Inc. is planning to purchase $346,000 worth of 6-year bonds issued by George Company, a publicly traded company on January 1,...

Q:

what would be the correct jounral entry The company received a notice from the bank related to a $100 NSF check deposited. Donald and Joe think the customer is good for this amount, and they believe...