Question Locate and describe the relative extrema, if any exist, of the function f(x, y) = 3.2² + 3y2 – 6x – 6y + 3 The critical point produces a Select an answer Preview Preview Hint: Enter an ordered triplet (1, y, z) into the final box.
37TB9P The Asker · Calculus
Transcribed Image Text: Locate and describe the relative extrema, if any exist, of the function f(x, y) = 3.2² + 3y2 – 6x – 6y + 3 The critical point produces a Select an answer Preview Preview Hint: Enter an ordered triplet (1, y, z) into the final box.
More Transcribed Image Text: Locate and describe the relative extrema, if any exist, of the function f(x, y) = 3.2² + 3y2 – 6x – 6y + 3 The critical point produces a Select an answer Preview Preview Hint: Enter an ordered triplet (1, y, z) into the final box.
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f(x, y)=3 x^{2}+3 y^{2}-6 x-6 y+3to find crictical point we need f_{x} and f_{y} then f_{x}=0, f_{y}=0then x, y are crictical pointcrictical pomt\begin{array}{l}f_{x}(x, y)=6 x-6=0 \Rightarrow x=1 \\f_{y}(x, y)=6 y-6=0 \Rightarrow y=1 \\r=f_{x x}(x, y)=6 \\S=f_{x y}(x, y)=0 \\t=f_{y y}(x, y)=6 \\\because r=6>0 \text { and } r t-s^{2}=36-0 \\=36>0\end{array}So f(1,1) to be a minimum value of f(x, x)cricticalpoin (1,1) minimum (1,1,-3)[\because f(1,1)=3+3-6-6+3] ...