ยง14.7 Extreme Values and Saddle Points

Lecture notes

Local extrema (first derivative test)

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Local extrema (second derivative test)

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Examples

  1. Find the local extrema and/or saddle points of $f(x,y)=x^2+2xy$.
  2. Find the local extrema and/or saddle points of $f(x,y)=x^2-2xy+2y^2-2x+2y+1$.
  3. Find the local extrema and/or saddle points of $f(x,y)=e^y-ye^x$.
  4. Find the local extrema and/or saddle points of $f(x,y)=\ln(x+y)+x^2-y$.
  5. Find the absolute extrema of \[ D(x,y)=x^2-xy+y^2+1 \] on the closed triangular plate in the first quadrant bounded by $x=0,\, y=4,\, x=y$.