Discuss the differentiability of f(x) =|x^3| at x=0.
Discuss the differentiability of f(x) =|x^3| at x=0.
Pawan joshi , 6 Years ago
Grade 12th pass
Differential Calculus> Discuss the differentiability of f(x) =|x...
1 Answers
Arun
Last Activity: 6 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.
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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