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
DanielleElmas [232]
3 years ago
5

Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 4y sqrt (x) , (4, 5) max

imum rate of change = ___________ direction vector = _________________
Mathematics
1 answer:
liubo4ka [24]3 years ago
4 0

Answer:

Remember that the maximum rate of change of f at a point u is the length of the of the gradient vector evaluate in u, and the direction in which it occurs is in direction of the gradient vector evaluate in u.

The gradient vector of f is

\triangledown f(x,y)=(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y})=(2yx^{-\frac{1}{2}}, 4\sqrt x)

Then, the maximum rate of change is|\triangledown f(4,5)|=|(2*5*4^{-\frac{1}{2}}, 4\sqrt 4)|=|(5,8)|=\sqrt{5^2+8^2}=\sqrt89 in the direction of (5,8).

You might be interested in
What do you think ? compared to bottoms up method: better, Worse, the same or something Else?
Leya [2.2K]
Idk what u mean.......
3 0
3 years ago
What are all the names that apply to <br> √24
Kisachek [45]

Answer: Square Root of 24

6 0
2 years ago
5x/3= -10<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B5x%7D%7B3%7D%20%20%3D%20%20-%2010" id="TexFormula1" title=" \frac{5x
Anastasy [175]
Solving for x
x= -30/5
x= -6 Answer
4 0
3 years ago
Which expression gives the solutions -5x+2x^2=-6x?(1pt)
irina [24]
This is the concept of algebra, the solution of the given expression will be given as follows;
-5x+2x²=-6x
adding 5x on both sides we get
5x-5x+2x²=-6x+5x
2x²=-x
divide both sides by 2
(2x²)/2=-x/2
x²=-x/2
divide both sides by x
(x²)/x=-x/(2x)
x=-1/2
the answer is x=-1/2
8 0
3 years ago
A water balloon is thrown out of a window 96 feet above the ground. The balloon is traveling downward at 16 feet per second init
gulaghasi [49]
It hits the ground at h=0

0=-16t^2-16t+96
undistribute -16
0=-16(t^2+t-6)
factor
0=-16(t-2)(t+3)
set to zero
0=t-2
2=t

t+3=0
t=-3, nope, we can't have negative time

at t=2, or 2 seconds
7 0
3 years ago
Read 2 more answers
Other questions:
  • brian made 16 paper cranes in 15 minutes.If he continues making cranes at this rate,how many cranes would he make in 2 hours?
    15·1 answer
  • Which of the following graphs shows all the possible values for a number that is less than 7? Number line with closed circle on
    12·1 answer
  • Choose the number sentence that shows the distributive property of multiplication over addition.
    11·1 answer
  • A company makes chocolate candies in the shape of a solid sphere. Each piece of candy has a diameter of 6cm. If a box contains 2
    5·2 answers
  • Someone help pls the topic is slope 10 points
    15·2 answers
  • 7/6 x 2/5, then put in simplest form
    12·2 answers
  • HELLLLLPPPP ASAP!!!!
    6·2 answers
  • .........................answer
    12·1 answer
  • 5 cakes shared between 3 people. what does each person recieved​
    10·1 answer
  • Start with x2 - 6x + 8 = 0 and complete the square, what is the equivalent equation?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!