Question

Given the functions f(x,y) = x3 + y3- 3x - 3y First find the coordinates of...

Given the functions f(x,y) = x3 + y3- 3x - 3y

First find the coordinates of all the critical points of f(x,y) and then apply the Second Order Partial Derivative Test to locate all relative maxima, relative minima and saddle points of f(x,y). Justify your answers and show your conclusions using an appropriate table.

[Hint: The domain of f(x,y) is an open region ]

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

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
If f(x,y)=(5∗x3+4∗y3+4∗x∗y+1) find the critical point for f(x,y) x=____ y=____ Is this critical point a local...
If f(x,y)=(5∗x3+4∗y3+4∗x∗y+1) find the critical point for f(x,y) x=____ y=____ Is this critical point a local maximum, local minimum, or saddle point?
Let f(x)=6x^2−2x^4. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates...
Let f(x)=6x^2−2x^4. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima). 1.   f is increasing on the intervals 2.   f is decreasing on the intervals 3.   The relative maxima of f occur at x = 4.   The relative minima of f occur at x =
f(x) = 3x + 2    Domain: ________________________________                 Graph: Range:   ________________________________ x-int: ______________ y-int: ___
f(x) = 3x + 2    Domain: ________________________________                 Graph: Range:   ________________________________ x-int: ______________ y-int: ______________ Maxima: _______________________________ Minima: ________________________________                                                                 Increasing: _____________________________ Decreasing: _____________________________ Constant: ______________________________ End Behavior: ___________________________ Discontinuities: __________________________ Asymptote: _____________________________ Symmetry: _____________________________ f(x) = ½ x – 4    Domain: ________________________________                 Graph: Range:   ________________________________ x-int: ______________ y-int: ______________ Maxima: _______________________________ Minima: ________________________________                                                                 Increasing: _____________________________   Decreasing: _____________________________ Constant: ______________________________ End Behavior: ___________________________ Discontinuities: __________________________ Asymptote: _____________________________ Symmetry: _____________________________ f(x) = x2 + x + 6    Domain: ________________________________                 Graph:...
f(x) = x3 – 3x2 + 10 Domain: ________________________________ Range: ________________________________ x-int: ______________ y-int: ______________ Maxima:...
f(x) = x3 – 3x2 + 10 Domain: ________________________________ Range: ________________________________ x-int: ______________ y-int: ______________ Maxima: _______________________________ Minima: ________________________________ Increasing: _____________________________ Decreasing: _____________________________ Constant: ______________________________ End Behavior: ___________________________ Discontinuities: __________________________ Asymptote: _____________________________ Symmetry: _____________________________Graph: f(t) = 2t4 – 10t2 + 12.5t Domain: ________________________________ : Range: ________________________________ x-int: ______________ y-int: ______________ Maxima: _______________________________ Minima: ________________________________ Increasing: _____________________________ Decreasing: _____________________________ Constant: ______________________________ End Behavior: ___________________________ Discontinuities: __________________________ Asymptote: _____________________________ Symmetry: _____________________________Graph: f(x) = 2x4 – 6x2 + 4.5 Domain: ________________________________ : Range:...
Given the function g(x) = x3-3x + 1, use the first and second derivative tests to...
Given the function g(x) = x3-3x + 1, use the first and second derivative tests to (a) Find the intervals where g(x) is increasing and decreasing. (b) Find the points where the function reaches all realtive maxima and minima. (c) Determine the intervals for which g(x) is concave up and concave down. (d) Determine all points of inflection for g(x). (e) Graph g(x). Label your axes, extrema, and point(s) of inflection.
Use the first derivative test to find the relative maxima and minima of the function f...
Use the first derivative test to find the relative maxima and minima of the function f (x) = 3x^4 + 8x^3 – 90x^2 + 1,200 on the domain (–∞, 7]. Determine the intervals of increase and decrease on this domain. Complete the answer box, if there are no answers, write “NONE.” SHOW WORK. Crit Points: Intervals of increase: Intervals of decrease: Coords of relative max Coords of relative min
(5) Let f(x, y) = −x^2 + 2x − 3y^3 + 6y^2 − 3y. (a) Find...
(5) Let f(x, y) = −x^2 + 2x − 3y^3 + 6y^2 − 3y. (a) Find both critical points of f(x, y). (b) Compute the Hessian of f(x, y). (c) Decide whether the critical points are saddle-points, local minimums, or local maximums.
Given f(x)= x3 - 6x2-15x+30 Determine f ’(x) Define “critical point” of a function. Then determine...
Given f(x)= x3 - 6x2-15x+30 Determine f ’(x) Define “critical point” of a function. Then determine the critical points of f(x). Use the sign of f ’(x) to determine the interval(s) on which the function is increasing and the interval(s) on which it is decreasing. Use the results from (c) to determine the location and values (x and y-values of the relative maxima and the relative minima of f(x). Determine f ’’(x) On which intervals is the graph of f(x)...
For each linear or quadratic functions, are required to find the domain, range, x-intercept, y-intercept, maxima,...
For each linear or quadratic functions, are required to find the domain, range, x-intercept, y-intercept, maxima, minima, end behavior, discontinuities, asymptote; asymmetry. Also graph the functions. Be sure to show all your work 1. f(x) = 3x+ 2 2. f(x) = 1/2X – 4
Let f(x, y) = 2x 3 − 6xy + y 2 − 4. Find all local...
Let f(x, y) = 2x 3 − 6xy + y 2 − 4. Find all local minima, local maxima, and saddle points of f(x, y).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT