http://www.xtremepapers.com/papers/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s11_qp_32.pdf Q 10 part iii how to do it !! i know its easy but i dont get it
first, when they told you the tangent at point P passes through the origin and if you draw a straight line ..to find the gradient you will do
(y-0)/(x-0) and so you will the gradient for the tangent at P = y/x
then, from the dy/dx equation you got above, make it equal to y/x
so ..
e^-x (-x^2+2x) = y/x
and multiply the x.. you will end up with y= e^-x (2x^2-x^3) ..this is your y!
substitute this y in the equation y=x^2e^-x to get
x^2e^-x = e^-x(2x^2 - x^3)
cancel the e^-x
you will get
x^2 = 2x^2 - x^3
-1x^2 = -1x
-1x=-1
so x=1