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The function $f(x)=e^{|x|}$ is

\begin{array}{1 1}(A)\;continuous \;everywhere \;but\;not\;differentiable\;at\;x=0\\(B)\;continuous\;and\;differentiable\;every where\\(C)\;not\;continuous\;at\;x=0\\(D)\;none\;of\;these.\end{array}

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Toolbox:
  • Every differentiable function is continuous,but the converse is not true.
  • A function is said to be differentiable at every point in its domain.
Step 1:
$f(x)=e^{\large |x|}$
For all values of $x$,the function is continuous,because $e^x$ is a continuous function at all points.
But when $x=0,e^{\large x}=e^0=1$
It becomes a constant.
Hence it is not differentiable.
The function is continuous everywhere,but not differentiable at $x=0$.
The correct option is $A$.
answered Jul 4, 2013 by sreemathi.v
 
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