I need help with these homework questions

1. Find all critical points of the given function.

f(x,y)=3x2+6y2+3xy42x+8

A. There are critical point(s) located at

enter your response here.

B. There are no critical points.

2. Find all points where the function has any relative extrema. Identify any saddle points.

f(x,y)=4x^2+2xy+y^2+6x+5

Find the derivatives fxx, fyy, and fxy.

fxx=

3. Find all points where the given function has any local extrema. Give the values of any local extrema. Identify any saddle points. ( I need to determine if a or b is correct for each question)

f(x,y)=x^26xy+y^2+18y+6

Find the local maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A.

There are local maxima located at

enter your response here. (Simplify your answer) OR B. There are no local maxima.

Find the value(s) of the local maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A.

The values of the local maxima are

enter your response here. (Simplify your answers. Use a comma to separate answers as needed.) OR B. There are no local maxima.

Find the local minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A.

There are local minima located at

enter your response here. (Simplify your answers. Type ordered pairs. Use a comma to separate answers as needed OR B. There are no local minima.

Find the value(s) of the local minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A.

The values of the local minima are

enter your response here.

(Simplify your answers) OR B. There are no local minima.

A.

There are saddle points located at

enter your response here.

(Simplify your answers) OR B. There are no saddle points.

4. Find all relative extrema for the function f(x,y)=3y^46y^2+3x^213

A. The relative maximum point(s) is(are) OR B. There are no relative maxima.

A. The value(s) of the function at the relative maximum point(s) is(are) OR B. There are no relative maxima.

A.

The relative minimum point(s) is(are) OR B. There are no relative minima.

A. The value(s) of the function at the relative minimum point(s) is(are) OR B. There are no relative minima.

A. The saddle point(s) is(are) OR B. There are no saddle points.

6. The profit (in thousands of dollars) from the sales of graphing calculators is approximated by

P(x,y)= 500 6x^3+ 12xy y^2 where x is the cost of a unit of chips and y is the cost of a unit of labor. Find the maximum profit and the costs of chips and labor that produce the maximum profit.

Find the maximum profit