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The curve $y=e^{-x} $ is

\[\begin{array}{1 1}(1)concave\;upward\;for \;x>0&(2)concave\;downward\;for\;x>0\\(3)every \;where\;concave\;upward &(4)every\;where\;concave\;downward\end{array}\]

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$\large\frac{dy}{dx}$$=-e^{-x} x-1=e^{-x}$
$\large\frac{d^2y}{dx^2}$$=-e^{-x} <0$ for all x
The given curve is concave downward every where
Hence 4 is the correct answer.
answered May 20, 2014 by meena.p
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