actical proplem (1) - Plot the following functions and find and characterize their critical points. (a) f( x1,x2)=x14+x24+1x12+x22 (b) f(x1,x2)=x12+x22+2x1x2 (c) f(x1,x2)=4x12+x22+x1x2+x1 (d) f(x1,x 2)=x14+x22+2x1x2x1x2 Hint: use contour() to plot the above functions such as fig, ax = plt.subplots (1,1) ax.contour (X,Y,f, levels=np. max(f)np.linspace(0,1.0,50)2) where f is defined by your function. For critical points, they are x1 and 2 values when f=0..

1. actical proplem (1) - Plot the following functions and find and characterize their critical points. (a) f(
x1,x2)=x14+x24+1x12+x22 (b) f(x1,x2)=x12+x22+2x1x2 (c) f(x1,x2)=4x12+x22+x1x2+x1 (d) f(x1,x
2)=x14+x22+2x1x2x1x2 Hint: use contour() to plot the above functions such as fig, ax =
plt.subplots (1,1) ax.contour (X,Y,f, levels=np. max(f)np.linspace(0,1.0,50)2) where f is defined by
your function. For critical points, they are x1 and 2 values when f=0.