Find the value of $x$ in $f (x) = x - e^{x}$ .

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Solution

$f (x) = x - e^{x}$
$f^{'} (x) = 1 - e^{x}$
Put $f^{'} (x) = 0$
$\Rightarrow 1 - e^{x} = 0$
$\Rightarrow e^{x} = 1$
$\Rightarrow e^{x} = e^{0}$
$∴ x = 0$

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