isi-entrance 2011 Q13

isi-entrance · India · solved Stationary points and optimisation Find critical points and classify extrema of a given function

Consider the function $f ( x ) = x ( x - 1 ) e ^ { 2 x }$ if $x \leq 0$ $f ( x ) = x ( 1 - x ) e ^ { - 2 x }$ if $x > 0$ Then $f ( x )$ attains its maximum value at
(a) $1 - 1 / \sqrt{2}$
(b) $1 + 1 / \sqrt{2}$
(c) $- 1 / \sqrt{2}$
(d) $1 / \sqrt{2}$

(C) $f(-1/\sqrt{2}) = (1/\sqrt{2})(1 + 1/\sqrt{2})e^{\sqrt{2}}$ which is greater than $f(1/\sqrt{2})$, $f(1-1/\sqrt{2})$, and $f(1+1/\sqrt{2})$.

Consider the function\\
$f ( x ) = x ( x - 1 ) e ^ { 2 x }$ if $x \leq 0$\\
$f ( x ) = x ( 1 - x ) e ^ { - 2 x }$ if $x > 0$\\
Then $f ( x )$ attains its maximum value at\\
(a) $1 - 1 / \sqrt{2}$\\
(b) $1 + 1 / \sqrt{2}$\\
(c) $- 1 / \sqrt{2}$\\
(d) $1 / \sqrt{2}$

Paper Questions

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