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Chapter 11: Partial Derivatives

Expert-verified
Essential Calculus: Early Transcendentals
Pages: 615 - 688
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

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Illustration

365 Questions for Chapter 11: Partial Derivatives

  1. \(3 - 14\)Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function.

    Found on Page 675

  2. Find and sketch the domain of the function \(f(x,y) = arcsin({x^2} + {y^2} - 2)\)

    Found on Page 623

  3. Determine the derivative \({W_s}(1,0)\) and\({W_t}(1,0)\). The functions are \(z = f(x,y),x = g(t)\) and \(y = h(t){\rm{. }}\)

    Found on Page 656

  4. \({\bf{1}} - {\bf{12}}\) Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint.

    Found on Page 683

  5. Find the first partial derivatives of the function.

    Found on Page 639

  6. Draw the graph of \(f\) and its tangent plane at the given point. (Use your computer algebra system both to compute the partial derivatives and to graph the surface and its tangent plane.) Then zoom in until the surface and the tangent plane become indistinguishable.

    Found on Page 648

  7. Find the directional derivative of the function at thegiven point in the direction of the vector\(v\).

    Found on Page 667

  8. Find the limit, if it exists, or show that the limit does not exist.

    Found on Page 632

  9. Find the limit, if it exists, or show that the limit does not exist.

    Found on Page 632

  10. \({\bf{1}} - {\bf{12}}\) Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint.

    Found on Page 683

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