This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y) = 4x + 8y; x2 + y2 = 20

(2,4) and (-2,-4).

Step-by-step explanation:

We consider the system

where g(x,y)=

gra(f(x,y))= (4,8)

gra(g(x,y))=(2x,2y)

So,

We have then that 4=2λx and 8=2λy. Dividing the second equation by 2 at both sides we obtain 4=λy. So, 4=2λx and 4=λy, we equalize both equations:

2λx=λy ⇔ 2x=y.

We replace that y value in the constraint equation:

and

With this two x values and the y equation y= 2x we can obtain the extremes: (2,4) and (-2,-4).

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!