Mathematics, 03.07.2019 09:30 janeliles

Find the local maximum and minimum values and saddle point(s) of the function. if you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (enter your answers as a comma-separated list. if an answer does not exist, enter dne.) f(x, y) = 9 - 2x + 4y - x2 - 4y2

Answers: 1

Show answers

Answers

Answer from: ipadguy1806

Solution:

There is no saddle point (DNE). However, there is local maximum at (1, 1/2) for the given function.

Explanation:

we have function of two variables f(x,y)= 9-2x+4y-x^2-4y^2

we will find the values by partial derivative with respect to x,y,xy

$f_{x}$ = -2 -2x

$f_{y}$ = 4 -8y

to find the saddle point we should first find the critical points so equate

-2 -2x=0 and 4 -8y=0

we get x= 1 and y =1/2 so, critical points are (1,1/2)

to find local maximum or minimum we have to find $f_{xx}$ , $f_{yy}$ and $f_{xy}$

formula is $f_{xx}$ * $f_{yy}$ - $f^{2_{xy} }$ =0

$f_{xx}$ = -2

$f_{yy}$ = -8

$f^{2_{xy} }$ =0

putting values in formula

(-2)*(-8) -0 =16 > 0, and $f_{xx}$ < 0 and $f_{yy}$ <0

so, here we have local maximum

we have no saddle point for this function by using the same formula we used to find extrema.

Find the local maximum and minimum values and saddle point(s) of the function. if you have three-dim

Answer from: qmsadler01

The point (-1,1/2) is a local maximum and there are no local minimums and saddle points.

Step-by-step explanation:

The function to study is f(x,y) = 9-2x+4y-x^2-4y^2 which is a differentiable function on the variables and . We find the possible points of local maximum, local minimum and saddle points finding the point where the partial derivatives are zero at the same time. So, we must calculate the partial derivatives:

$\frac{\partial f}{\partial x} = -2-2x = -2(x+1)$

$\frac{\partial f}{\partial y} = 4-8y = 4(1-2y)$

It is not difficult to see that the only point where $\frac{\partial f}{\partial x}(x,y)=\frac{\partial f}{\partial y}(x,y) =0$ is (-1,1/2). Notice that the system of equations

$\begin{cases} -2(x+1) &= 0\\ 4(1-2y) &= 0\end{cases}$

has solution x= -1 and y=1/2.

If we want to know if (-1,1/2) is local maximum, local minimum or saddle point we must calculate the partial derivatives of second order:

$\frac{\partial^2 f}{\partial x^2} = -2 = A$

$\frac{\partial^2 f}{\partial y^2} = -8 = B$

$\frac{\partial^2 f}{\partial y \partial x} = \frac{\partial^2 f}{\partial x \partial y} = 0 = C$ .

Substituting the values into the formula AB-C^2 we get (-2)(-8)-0=16>0. As the value we have obtained is greater than zero and A=-2<0 we assure that the point (-1,1/2) is a local minimum.

There are no local maximums or saddle points.

Answer from: Quest

A= r2 × 3.14 11×11 ↓ ↓ 121 × 3.14 = 379.94 → 379.9

Answer from: Quest

answer: 20

step-by-step explanation: subtract the minimum date value from the maximum data value to find the date range. in this casem the date range is 42 - 22 = 20

hope this ! : ) ~zane

Another question on Mathematics

Mathematics, 21.06.2019 14:30

What is the inverse of the function f(x)=4x+8

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

What is the value of x in the following equation? -3x-2=2x+8

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

The paint recipe also calls for 1/4 cup of food coloring. tyler says mrs.mcglashan will also need 6 cups of food coloring. do u agree or disagree? explain.

Answers: 2

Answer

Mathematics, 21.06.2019 22:20

1. 2. ∠b and ∠y are right angles. 3.? 4.? which two statements are missing in steps 3 and 4? ∠x ≅ ∠c △abc ~ △zyx by the sas similarity theorem. ∠b ≅ ∠y △abc ~ △zyx by the sas similarity theorem. = 2 △abc ~ △zyx by the sss similarity theorem. = 2 △abc ~ △zyx by the sss similarity theorem.

Answers: 2

Answer

You know the right answer?

Find the local maximum and minimum values and saddle point(s) of the function. if you have three-dim...

Questions