2 inches
2 answers:
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Answer:
The points are (0,0) Minimum
(1/6, 1/18) Saddle point
Step-by-step explanation:
To solve the question we have
f(x,y) = xy(1-2x-6y)
Therefore, f(x,y) = xy-2x²y-6xy²
Finding the partial derivative of the above gives
fₓ = y - 4xy-6y²
= x - 2x²-12xy
Therefore, when the above equations are set to 0 we get
y - 4xy-6y² = 0.......(1)
x - 2x²-12xy = 0......(2)
Dividing equation (1) and (2) by y and x respectively gives
1 - 4x - 6y = 0
1 - 2x - 12y = 0
Solving gives
x = 0.167 = 1/6
y = 0.056 = 1/18
When we place x in equation (1) we have
y - 4(1/6)y-6y² = 0
y = 0 or y = 1/18
Similarly, x = 0 or 1/6
Therefore, the four critical points are
(0,0) (1/6,1/18)
When x = 0 and y = 0
f(x,y) = 0 Hence this is a minimum
When x = 1/6 and y = 1/18
f (x,y) = 1/324 Which is a saddle point.