Let f(x)=|x| and g(x)=|x^3| , then f(x) ...

Let `f(x)=|x|` and `g(x)=|x^3|` , then `f(x)` and `g(x)` both are continuous at `x=0` (b) `f(x)` and `g(x)` both are differentiable at `x=0` (c) `f(x)` is differentiable but `g(x)` is not differentiable at `x=0` (d) `f(x)` and `g(x)` both are not differentiable at `x=0`

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`f(x)=|x| ` and `g(x)=|x^3|`
Both are continuous at `x=0`
`f'(x)=x/|x| implies f(x)` is not differentiable at `x=0`
But `g'(x)=x^3/|x^3|xx3x^2=0`
`implies g(x) ` is differentiable at `x=0`
Hence, option (a) is correct.

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