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SSC Pure Mathematics QUESTION #4105
Question 1
The absolute maximum value of \(f(x,y)=xy-2x\) over the entire triangular region with vertices \((0,0),(4,0),(0,4)\) is:
  • \(0\)
  • \(1\)✔️
  • \(4\)
  • \(8\)
Correct Answer Explanation
Boundary analysis: Edge \(y=0\): \(f=-2x\leq0\). Edge \(x=0\): \(f=0\). Edge \(y=4-x\): \(f=-x^2+2x\), max at \(x=1\) giving \(f=1\). Vertex values: \(f(0,0)=0\), \(f(4,0)=-8\), \(f(0,4)=0\). The absolute maximum is \(\boxed{1}\) at \((1,3)\).