A curve has the equation \(y=\dfrac{e^{2x}(3x+2)}5\).
Find the \(x\)-coordinate(s) of the stationary point of the curve.[5]
Find \(\dfrac{\mathrm d^2y}{\mathrm dx^2}\) and hence determine the nature of the stationary point.[4]
Explain why given that when \(x>-1\), the gradient of the curve is positive.[2]