Moderate -0.8 This is a straightforward application of the quotient rule to find dy/dx, followed by routine evaluation at x=0 to find the gradient and y-coordinate, then forming the tangent equation. All steps are standard with no problem-solving required, making it easier than average but not trivial due to the exponential function and algebraic manipulation needed.
4 Find the equation of the tangent to the curve \(y = \frac { \mathrm { e } ^ { 4 x } } { 2 x + 3 }\) at the point on the curve for which \(x = 0\). Give your answer in the form \(a x + b y + c = 0\) where \(a , b\) and \(c\) are integers.
4 Find the equation of the tangent to the curve $y = \frac { \mathrm { e } ^ { 4 x } } { 2 x + 3 }$ at the point on the curve for which $x = 0$. Give your answer in the form $a x + b y + c = 0$ where $a , b$ and $c$ are integers.\\
\hfill \mbox{\textit{CAIE P2 2017 Q4 [5]}}