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If f(x)=|x|^3 , show that f"(x) exists f...

If `f(x)=|x|^3` , show that `f"(x)` exists for all real `x` and find it.

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To solve the problem, we need to show that the second derivative \( f''(x) \) exists for all real \( x \) and find its value. The function given is \( f(x) = |x|^3 \). ### Step 1: Define the function in different intervals The absolute value function can be expressed piecewise: \[ f(x) = \begin{cases} ...
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