For full credit indicate clearly how you reached your answer.

[3 pts] 1. Use Lagrange multipliers to find the minimum value of the function f(x,y) = x² + y² on the line y = -3x + 2.
 
 

[3 pts] 2. Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y) = x² + y² on the curve x⁴ + y⁴ = 1.
 

[3 pts] 3. Use Lagrange multipliers to find the maximum value of f(t,m)=  subject to the constraint m = 60t-480.
 
 

[3 pts] 4. Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y,z) = x - y +3z on the surface x² + y² + 4z² = 4.
 
 

[2 pts] 5. Find .
 
 

[2 pts] 6. Find .
 
 

[2 pts] 7. Find .
 
 

[2 pts.] 8. Find .