Question:
Show that the lagrange's mean value theorem is not applicable to the function
$f(x)=\frac{1}{x}$ on $[-1,1]$
Solution:
Given:
$f(x)=\frac{1}{x}$
Clearly, $f(x)$ does not exist for $x=0$
Thus, the given function is discontinuous on $[-1,1]$.
Hence, Lagrange's mean value theorem is not applicable for the given function on $[-1,1]$.
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