Standard +0.8 This is a Further Maths question requiring partial derivatives to find the tangent plane to a surface. While the technique is standard (compute ∂z/∂x and ∂z/∂y, then use the tangent plane formula), the algebraic manipulation with mixed powers (x√y and y√x terms) adds moderate complexity. It's above average difficulty due to being Further Maths content with non-trivial differentiation, but remains a straightforward application of a learned method.
2 A surface \(S\) has equation \(\mathrm { z } = 4 \mathrm { x } \sqrt { \mathrm { y } } - \mathrm { y } \sqrt { \mathrm { x } } + \mathrm { y } ^ { 2 }\) for \(x , y \geqslant 0\).
Determine the equation of the tangent plane to \(S\) at the point (1,4,20). Give your answer in the form \(\mathrm { ax } + \mathrm { by } + \mathrm { cz } = \mathrm { d }\) where \(a , b , c\) and \(d\) are integers.
2 A surface $S$ has equation $\mathrm { z } = 4 \mathrm { x } \sqrt { \mathrm { y } } - \mathrm { y } \sqrt { \mathrm { x } } + \mathrm { y } ^ { 2 }$ for $x , y \geqslant 0$.
Determine the equation of the tangent plane to $S$ at the point (1,4,20). Give your answer in the form $\mathrm { ax } + \mathrm { by } + \mathrm { cz } = \mathrm { d }$ where $a , b , c$ and $d$ are integers.
\hfill \mbox{\textit{OCR Further Additional Pure 2024 Q2 [5]}}