Moderate -0.8 This is a straightforward differentiation and normal line question requiring basic power rule (including fractional powers), substitution to find gradient and point coordinates, then using perpendicular gradient formula. All steps are routine A-level techniques with no conceptual challenges, making it easier than average but not trivial due to the arithmetic involved with fractions.
6. The curve \(C\) has the equation \(y = 6 x ^ { 2 } + 2 \sqrt { x }\). Find the equation of the normal of the curve at the point where \(x = \frac { 1 } { 4 }\), giving your answer in the form \(a x + b y = k\) where \(a , b\) and \(k\) are positive integers.
For this question, show detailed reasoning with your working [0pt]
6. The curve $C$ has the equation $y = 6 x ^ { 2 } + 2 \sqrt { x }$. Find the equation of the normal of the curve at the point where $x = \frac { 1 } { 4 }$, giving your answer in the form $a x + b y = k$ where $a , b$ and $k$ are positive integers.
For this question, show detailed reasoning with your working\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM 2022 Q6 [5]}}