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Discuss the differentiability of f(x) =|x^3| at x=0.

Discuss the differentiability of f(x) =|x^3| at x=0.

Grade:12th pass

1 Answers

Arun
25763 Points
2 years ago
Yes.
 
The easiest way to show this to consider the functions y = x^3 and y =(-x)^3 being the right and left sides of the graph.
 
The derivative of y = x^3 is 3x^2, and its value at x = 0 is 0.
The derivative of (-x)^3 is -3x^2, and its value at x = 0 is also 0.
 
Hence the derivative is the same when approached from the left or the right.

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