A) \[f(x)=\tan ({{x}^{2}}),\,x\in [3,\,4]\]
B) \[f(x)=\tan x,\,x\in [1,\,3]\]
C) \[f(x)=\sin (4{{x}^{3}}-5{{x}^{2}}+x-2),\,x\in [0,1]\]
D) \[f(x)={{x}^{4/5}}{{(x-1)}^{1/5}},\,x\in \left[ -\frac{1}{2},\,\frac{1}{2} \right]\]
Correct Answer: C
Solution :
\[\sin (4{{x}^{3}}-5{{x}^{2}}+x-2)\] is differentiable in R. \[\tan ({{x}^{2}})\] is not defined at \[\sqrt{\frac{7\pi }{2}}\]. \[\tan (x)\] is not defined at \[\frac{\pi }{2}\]. \[{{x}^{4/5}}{{(x-1)}^{1/5}}\] is not differentiable at \[x=0\].
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