SOLUTION: A curve has an equation of {{{y=xe^x}}}. The curve has a stationary point at P. (i)Find,in terms of e, the coordinates of P and determine the nature of this stationary point. The

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Question 912018: A curve has an equation of . The curve has a stationary point at P.
(i)Find,in terms of e, the coordinates of P and determine the nature of this stationary point.
The normal to the curve at the point Q (1,e) meets the x-axis at R and the y-axis at S.
(ii)Find in terms of e, the area of the triangle ORS, where O is the origin.
Answer by Alan3354(69443) (Show Source):
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A curve has an equation of . The curve has a stationary point at P.
(i)Find,in terms of e, the coordinates of P and determine the nature of this stationary point.
y' =

e^x = 0 (Ignore)
x = -1 is a local minimum
y = 1/e
(-1,1/e) is a local minimum
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The normal to the curve at the point Q (1,e) meets the x-axis at R and the y-axis at S.
(ii)Find in terms of e, the area of the triangle ORS, where O is the origin.
y' =
y'(1) = 2e
m of the normal = -1/(2e)
y - e = (-1/2e)*(x - 1) = -x/(2e) + 1/(2e)

--> S((2e^2 + 1)/(2e),0)
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x = 2e^2 + 1 --> R(2e^2 + 1,0)
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Area = bh/2
=
=