OCR Further Additional Pure AS 2017 December — Question 8

Exam BoardOCR
ModuleFurther Additional Pure AS (Further Additional Pure AS)
Year2017
SessionDecember
TopicInvariant lines and eigenvalues and vectors

8 A surface \(S\) has equation \(z = 8 y ^ { 3 } - 6 x ^ { 2 } y + 60 x y - 15 x ^ { 2 } + 186 x - 150 y - 100\).
  1. (a) Find any stationary points of the section of \(S\) given by \(y = - 3\).
    (b) Find any stationary points of the section of \(S\) given by \(x = - 1\).
  2. Show that the surface \(S\) has a least one saddle point. \section*{OCR} Oxford Cambridge and RSA