Answer:
Solution has explained below:
Step-by-step explanation:
(a) f(x,y) = x+y
To find out the maximum and minimum values, we need to find first and second derivatives, we have
fx= 1, fx₁=0 and
fy= 1 and fyy=0
For stationary points fx=fy=0, which gives,
1=1=0, so that there is just one stationary point, (x,y)=(0,0)
If fx₁ < 0 and fyy < 0, function is maximum
If fx₁ > 0 and fyy > 0, function is minimum.
(b) g(x,y) = xy
Sol: To find out the maximum and minimum values, we need to find first and second derivatives, we have
fx= 1 and fy = 1
fx₁ = 0 and fyy =0
for stationary points fx = fy =0, which gives 1=1=0, so that there is just one stationary points, (x,y) =(0,0)
If fx₁ < 0 and fyy < 0, function is maximum.
If fx₁ > 0 and fyy> 0, function is minimum.
c) h(x,y) = 2x2 + y2
sol: To find out the maximum and minimum values, we need to find first and second derivatives, we have
fx = 4x and fy = 2y
fx₁= 4 and fyy = 2
Now, taking fx = 0 and fy = 0
Gives x=0 and y=0,
Stationary points are (x,y) = (0,0)
If fx₁ < 0 and fyy < 0, solution is maximum,
If fx₁ > 0 and fyy > 0, solution is minimum,
Here, fx₁ = 4 > 0 and fyy = 2 > 0.
