Paper 3 May/June 2008 MATHEMATICH (9709/3) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

A certain curve is such that its gradient at a point $\left( {x,{\text{ }}y} \right)$ is proportional to $xy$. At the point $\left( {1,{\text{ }}2} \right)$ the gradient is 4.
a) By setting up and solving a differential equation, show that the equation of the curve is $y = 2{e^{{x^2} - 1}}$..
b) State the gradient of the curve at the point $\left( { - 1,{\text{ }}2} \right)$ and sketch the curve.