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

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

= -2 -2x

= 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 ,   and

formula is * - =0

= -2

= -8

=0

putting values in formula

(-2)*(-8) -0 =16 > 0, and < 0  and <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.

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 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:

It is not difficult to see that the only point where is (-1,1/2). Notice that the system of equations

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:

.

Substituting the values into the formula 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.

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2

answer: c.  

step-by-step explanation:

mixtures containing substances that get attracted to magnet can be separated using a magnet. we can separate iron from a mixture of sand and iron, as only iron attracts to the magnet.