4. The straight line with equation \(y = 4 x + c\), where \(c\) is a constant, is a tangent to the curve with equation \(y = 2 x ^ { 2 } + 8 x + 3\) Calculate the value of \(c\) $$\begin{aligned} & y = m x + c \rightarrow y = 4 x + c \quad ( m = 4 )
& \therefore \frac { d y } { d x } = 4 x + 8 = 4 \quad \text { (Gradient equation) }
& 4 x + 8 = 4
& x = - 1 \rightarrow y = - 3
& \text { At } ( - 1 , - 3 ) - 3 = 4 ( - 1 ) + c
& \quad c = 1
& y = 4 x + 1 \end{aligned}$$ \section*{PMT PhysicsAndMathsTutor.com}