4.01: Exponential curve, tangent and integral
A curve has equation \(y=x\mathrm{e}^{2x+1}\).
(a)[3]
Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\).
See the official mark scheme below.
(b)[5]
The line \(L\) is the tangent to the curve at the point where \(x=\dfrac12\). Find the exact coordinates of the two points where \(L\) meets the axes.
See the official mark scheme below.
(c)[4]
Use your answer to part (a) to find \(\displaystyle\int x\mathrm{e}^{2x+1}\,\mathrm{d}x\).
See the official mark scheme below.
