(Solved): I need full answer of all parts of this question Question 1 [30 pts] Given the function of two va ...

I need full answer of all parts of this question

Question 1 [30 pts] Given the function of two variables \[ f(x, y)=-8 x^{2}-6 x y-8 y^{2}-4 \] a) [10 pts] Use Lagrange Multipliers to find the extreme value(s) of the function \( f \) subject to the constraint \( 3 x+y+3=0 \). b) \( [\mathbf{1 0} \) pts] Verify that \( f(x, y)= \) \[ -\frac{1}{8}(8 x+3 y)^{2}-\left(\frac{55}{8} y^{2}+4\right) \] c) \( [\mathbf{1 0} \) pts] Show that \( f \) has maximum and no minimum with the constraint \( 3 x+y+3=0 \).