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CSS Pure Mathematics QUESTION #1282
Question 1
For the second derivative test, a critical point \((a,b)\) is a saddle point if \(D=f_{xx}f_{yy}-(f_{xy})^2\) satisfies:
  • D > 0 and \(f_{xx}>0\)
  • D > 0 and \(f_{xx}<0\)
  • D < 0✔️
  • D = 0
Correct Answer Explanation
The second derivative test: if \(D>0\) and \(f_{xx}>0\): local minimum; if \(D>0\) and \(f_{xx}<0\): local maximum; if \(D<0\): saddle point; if \(D=0\): test is inconclusive.