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The set of all points where the function `f(x)=3sqrt(x^2|x|)` is differentiable, isA. `[0,oo)`B. `(0,oo)`C. `(-oo,oo)`D. `(-oo0) uu (0,oo)` |
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Answer» Correct Answer - D We have `f(x)=(x^(2)|x|)^(1//3)` `Rightarrow f(x)={{:(,(-x^(3))^(1//3)=-x, x lt 0),(,(x^(3))^(1//3)=x,x ge0):}` `Rightarrow f(x)=|x|` Clearly , it is everywhere differentiable except at x=0. Hence, the set of all points where f(x) is differentiable is `R-(0)=(-oo, 0) uu (0,oo)` |
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