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Worksheet: Finding the Stationary Points of Two Variable Function

Q1:

Find all stationary points of the function , stating whether they are minima, maxima, or saddle points.

  • Alocal minimum at
  • Blocal maximum at
  • Csaddle point at
  • DThe function has no stationary points.

Q2:

Find all stationary points of the function .

  • A is a local minimum point, is a local maximum point, and and are saddle points.
  • B is a local minimum point, is a local maximum point, and and are saddle points.
  • C and are local mimimum points, is a local maximum point, and is a saddle point.
  • D is a local minimum point, is a local maximum point, and and are saddle points.
  • E is a local minimum point, and are local maximum points, and is a saddle point.

Q3:

Find all local maxima and minima of the function .

  • Alocal maximum at , saddle point at
  • Blocal minimum at , saddle point at
  • Clocal maximum at , saddle point at
  • Dlocal minimum at , saddle point at
  • Elocal minimum at , saddle point at

Q4:

Find all stationary points of the function , stating whether they are minima, maxima, or saddle points.

  • A is a local minimum point.
  • B is a local maximum point.
  • C is a saddle point.
  • D is a local minimum point.
  • E is a local maximum point.

Q5:

Find all stationary points of the function , stating whether they are minima, maxima, or saddle points.

  • A and are local minimum points.
  • B and are local maximum points.
  • C is a local maximum point and is a saddle point.
  • D is a local minimum point and is a saddle point.
  • E and are saddle points.

Q6:

Find all stationary points of the function , stating whether they are minima, maxima, or saddle points.

  • A is a local minimum point and is a saddle point.
  • B is a local maximum point and is a saddle point.
  • C is a local maximum point and is a saddle point.
  • D is a local minimum point and is a saddle point.
  • E is a local minimum point and is a saddle point.

Q7:

Find all stationary points of the function , stating whether they are minima, maxima, or saddle points.

  • A is a local minimum point and is a saddle point.
  • B is a local minimum point and is a saddle point.
  • C is a local minimum point and is a saddle point.
  • D is a local minimum point and is a saddle point.
  • E is a local minimum point and is a saddle point.

Q8:

Find all stationary points of the function , stating whether they are minima, maxima, or saddle points.

  • A is a local minimum point, is a local maximum point, and and are saddle points.
  • B is a local minimum point, is a local maximum point, and and are saddle points.
  • C and are local minimum points, is a local maximum point, and is a saddle point.
  • D is a local minimum point, is a local maximum point, and and are saddle points.
  • E is a local minimum point, and are local maximum points, and is a saddle point.

Q9:

Find all stationary points of the function , stating whether they are minima, maxima, or saddle points.

  • A is a saddle point.
  • B is a local minimum point.
  • C is a local maximum point.
  • D is a local maximum point.
  • E is a local minimum point.