Use the method of lagrange multipliers to end the maximum and minimum values of the function subject to the given constraints: f(x, y, z) = yz + xy xy = 1 y^2 + z^2 = 1

Looks like you're looking for the extrema of subject to and . The Lagrangian is

Look for any critical points:

(we don't want )

but then so we omit this case.

Now,

The first two critical points give a minimum value of , and the other two give a maximum value of .

4x and 6y

im not sure though

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?