Question

The function f ( x , y ) = x 3 + 27 x y 2...

The function

f ( x , y ) = x 3 + 27 x y 2 − 27 x

has partial derivatives given by
f x = 3 x 2 + 27 y 2 − 27,
f y = 54 x y,
f x x = 6 x,
f y y = 54 x,
f x y = 54 y, and
f y x = 54 y,

AND has  as a critical point. (You need NOT check this.)

Use the second derivative test to classify the point :

  

A.None of the other answers

B.Local maximum

   

C.Saddle point

   

D.Local minimum

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

kindly please upvote this

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the function f : R 2 → R defined by f(x, y) = 4 +...
Consider the function f : R 2 → R defined by f(x, y) = 4 + x 3 + y 3 − 3xy. (a)Compute the directional derivative of f at the point (a, b) = ( 1 2 , 1 2 ), in the direction u = ( √ 1 2 , − √ 1 2 ). At the point ( 1 2 , 1 2 ), is u the direction of steepest ascent, steepest descent, or neither? Justify your...
You are given that the function f(x,y)=8x2+y2+2x2y+3 has first partials fx(x,y)=16x+4xy and fy(x,y)=2y+2x2, and has second...
You are given that the function f(x,y)=8x2+y2+2x2y+3 has first partials fx(x,y)=16x+4xy and fy(x,y)=2y+2x2, and has second partials fxx(x,y)=16+4y, fxy(x,y)=4x and fyy(x,y)=2. Consider the point (0,0). Which one of the following statements is true? A. (0,0) is not a critical point of f(x,y). B. f(x,y) has a saddle point at (0,0). C. f(x,y) has a local maximum at (0,0). D. f(x,y) has a local minimum at (0,0). E. The second derivative test provides no information about the behaviour of f(x,y) at...
Problem 1. (1 point) Find the critical point of the function f(x,y)=−(6x+y2+ln(|x+y|))f(x,y)=−(6x+y2+ln(|x+y|)). c=? Use the Second...
Problem 1. (1 point) Find the critical point of the function f(x,y)=−(6x+y2+ln(|x+y|))f(x,y)=−(6x+y2+ln(|x+y|)). c=? Use the Second Derivative Test to determine whether it is A. a local minimum B. a local maximum C. test fails D. a saddle point
The function f(x) = x^3+ax^2+bx+7 has a relative extrema at x = 1 and x =...
The function f(x) = x^3+ax^2+bx+7 has a relative extrema at x = 1 and x = -3. a.) What are the values of a and b? b.) Use the second derivative test to classify each extremum as a relative maximum or a relative minimum. c.) Determine the relative extrema.
Examine the function f(x, y) = 2x 2 + 2xy + y 2 + 2x −...
Examine the function f(x, y) = 2x 2 + 2xy + y 2 + 2x − 3 for relative extrema. Use the Second Partials Test to determine whether there is a relative maximum, relative minimum, a saddle point, or insufficient information to determine the nature of the function f(x, y) at the critical point (x0, y0), such that fxx(x0, y0) = −3, fyy(x0, y0) = −8, fxy(x0, y0) = 2.
Given f(x,y) = x2−3y2−8x+9y+3xy  for each and any point that is critical, use the second-partial-derivative test to...
Given f(x,y) = x2−3y2−8x+9y+3xy  for each and any point that is critical, use the second-partial-derivative test to determine whether the point is a relative maximum, relative minimum, or a saddle point.
The derivative of the function f(x) is given by: ?′(?)=−3?2+18?−24 Classify the maximum and minimum stationary...
The derivative of the function f(x) is given by: ?′(?)=−3?2+18?−24 Classify the maximum and minimum stationary (turning) points for this function.
Find the directional derivative of the function f(x,y)=x^6+y^3/(x+y+6 ) at the point (2,-2) in the direction...
Find the directional derivative of the function f(x,y)=x^6+y^3/(x+y+6 ) at the point (2,-2) in the direction of the vector < - 2 ,2>. b) Also find the maximum rate of change of f at the given point and the unit vector of the direction in which the maximum occurs.
f(x)=x^3-4x^2+5x-2 Find all critical numbers of the function, then use the second derivative test on each...
f(x)=x^3-4x^2+5x-2 Find all critical numbers of the function, then use the second derivative test on each critical number to determine if it is a local maximum or minimum. Show your work.
part 1) Find the partial derivatives of the function f(x,y)=xsin(7x^6y): fx(x,y)= fy(x,y)= part 2) Find the...
part 1) Find the partial derivatives of the function f(x,y)=xsin(7x^6y): fx(x,y)= fy(x,y)= part 2) Find the partial derivatives of the function f(x,y)=x^6y^6/x^2+y^2 fx(x,y)= fy(x,y)= part 3) Find all first- and second-order partial derivatives of the function f(x,y)=2x^2y^2−2x^2+5y fx(x,y)= fy(x,y)= fxx(x,y)= fxy(x,y)= fyy(x,y)= part 4) Find all first- and second-order partial derivatives of the function f(x,y)=9ye^(3x) fx(x,y)= fy(x,y)= fxx(x,y)= fxy(x,y)= fyy(x,y)= part 5) For the function given below, find the numbers (x,y) such that fx(x,y)=0 and fy(x,y)=0 f(x,y)=6x^2+23y^2+23xy+4x−2 Answer: x= and...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT