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Q.
The function $f(x) = | x^3 |$ is
Continuity and Differentiability
Solution:
The range of the function $x^3$ is $(- \infty, \infty)$, and the range of $f (x)$ is $[0, \infty)$, f is clearly differentiable except possibly at the point $x = 0$. Now, clearly by definition $R f '(0) = L\, f' (0) = 0$ so that, f is differentiable at $x = 0$ and hence everywhere.