A) the function is not continuous at\[x=8\]
B) \[f(0)\ne f(16)\]
C) the function is not differentiable at \[x=8\]
D) the function is not differentiable at all points in \[(0,\,16)\]
Correct Answer: C
Solution :
Given, function \[f(x)=|x-8|,\,0\le x\le 16\] This function is continuous at \[x=8,\] since \[LHL=RHL=f(8)\] Also, \[f(0)=f(16)=8\] But, this function is not differentiable at \[x=8.\] Hence, for the given function Rolle?s theorem is not applicable, since the function is not differentiable at \[x=8.\]You need to login to perform this action.
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