aplications f derivatives

point "A" lies on d curve y=e^-x²and has d

coordinates{x,e^-x²} wer x>0.point B has d

coordinates{x,0}.if O iz d origin then the max area of triangle

AOB is a)1/âˆš2e b)1/âˆš4e c)1/âˆše d)1/âˆš8e

2 Answers

d)1/âˆš8e is the answer ..

{x,e-x2} , {x,0} , {0,0} ...
Area is given by ...
mod(x*(0-0) + x*(0 - e^-x²) + 0*(e^-x² - 0) )/2

xe^-x²/2 = Area
differentiating this we get
e^-x² - 2x²e^-x² =0

x = 1/âˆš2

putting this in the original eq of area we get the answer .....

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