OCR Further Additional Pure 2021 November — Question 5

Exam BoardOCR
ModuleFurther Additional Pure (Further Additional Pure)
Year2021
SessionNovember
TopicVector Product and Surfaces

5 The surface \(S\) has equation \(x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = x y z - 1\).
  1. Show that \(( 2 z - x y ) \left( x \frac { \partial z } { \partial x } + y \frac { \partial z } { \partial y } \right) = 2 \left( 1 + z ^ { 2 } \right)\).
  2. Deduce that \(S\) has no stationary point.