1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
labwork [276]
3 years ago
8

Consider the following. f(x, y, z) = x2yz − xyz8, P(6, −1, 1), u = 0, 4 5 , − 3 5 (a) Find the gradient of f. ∇f(x, y, z) = (b)

Evaluate the gradient at the point P. ∇f(6, −1, 1) = (c) Find the rate of change of f at P in the direction of the vector u. Duf(6, −1, 1) =
Mathematics
1 answer:
Darina [25.2K]3 years ago
5 0

Answer:

a)  ∇f(x, y, z) = (2xyz − yz⁸, x²z − xz⁸, x²y − 8xyz⁷)

b)  ∇f(6, −1, 1) = (-11, 30, 12)

c)  Duf(6, −1, 1) = 84/5

Step-by-step explanation:

Given

f(x, y, z) = x²yz − xyz⁸

P(6, −1, 1)

u = (0, 4/5, − 3/5)

a) ∇f(x, y, z) = ?

We apply

fx(x, y, z) = 2xyz − yz⁸

fy(x, y, z) = x²z − xz⁸

fz(x, y, z) = x²y − 8xyz⁷

then

∇f(x, y, z) = (2xyz − yz⁸, x²z − xz⁸, x²y − 8xyz⁷)

b) ∇f(6, −1, 1) = (2*6*(-1)*1 − (-1)(1)⁸, (6)²(1) − (6)(1)⁸, (6)²(-1) − 8(6)(-1)(1)⁷)

⇒  ∇f(6, −1, 1) = (-11, 30, 12)

c) Duf(6, −1, 1) = ∇f(6, −1, 1)*(0, 4/5, − 3/5) = (-11, 30, 12)*(0, 4/5, − 3/5)

⇒  Duf(6, −1, 1) = 0 + 24 - 36/5 = 84/5

You might be interested in
Rolling a number less than 4 on a number cube labeled 1 through 6
olga_2 [115]
Rolling a number less than 4 means that rolling a 1, 2, or 3 will satisfy the requirement. Since 3 of 6 possible outcomes will satisfy the requirement then the likelihood that it will be rolled is 3/6 times. 3/6 reduces to 1/2 or 50% chance.
3 0
3 years ago
At which root does the graph of f(x) = (x + 4)(x + 7,5) cross the x-axis?<br> -7<br> -4<br> 4<br> 7
Alona [7]

Answer:

Answer: -7

Step-by-step explanation:

5 0
2 years ago
for the given kite find the length of side LM write your answer in simplest radical form. show all work.
Gnesinka [82]

Answer:

13sqrt(2) units

Step-by-step explanation:

LM² = 7² + 17²

LM² = 338

LM = sqrt(338)

LM = 13sqrt(2)

sqrt: square root

3 0
3 years ago
Can one of you guys help me please :( thank you
timurjin [86]

Answer:

42???

Step-by-step explanation:

sorry if wrong

hope this helps

5 0
3 years ago
Read 2 more answers
The diameter of a basketball is 9.50 inches. What is the volume of the ball, rounded to the nearest hundredth?
Lady_Fox [76]
448.92 cubic inches tell me if im right

8 0
3 years ago
Read 2 more answers
Other questions:
  • What is the solution for the system of equations? Use the substitution method to solve. 2x+y=20
    11·1 answer
  • Help last question!!! Please
    15·1 answer
  • Solve the following inequality.<br><br> IMAGE ATTACHED
    8·1 answer
  • A sofa is selling for $422.50 after a 35% discount . What was the original price for the sofa ?
    5·1 answer
  • What is less than 1/2
    12·1 answer
  • Which of the following best describes the lines y = 5 and
    8·1 answer
  • Please help with finding what quandrant theta is in? (Problem 8)
    8·1 answer
  • Examine the diagram.
    14·2 answers
  • Please SOMEONE tell me if i picked the correct one ):
    5·2 answers
  • Factorize<br>a)a²x+2ax-3x+5a²+10a-15<br>b)(a+b)(a-b)-a+b<br>c)x³-x²+x+x²y-xy+y​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!