For what values of x is │x^2-4│ not differentiable?

Thread starter gillgill
Start date Apr 17, 2005
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Differentiable

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The function │x^2-4│ is not differentiable at x = -2 and x = 2, where the left-hand and right-hand limits of the derivative differ. To determine these points, one can differentiate the function and analyze where the derivative fails to exist. The definition of the derivative, involving limits, is essential for this analysis. Therefore, the critical values where differentiability is lost are specifically at these two points. Understanding these concepts is crucial for evaluating the differentiability of absolute value functions.

Apr 17, 2005

gillgill

For what values of x is │x^2-4│ not differentiable?
Is there a way to solve it without looking at the graph?

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Apr 17, 2005

Hurkyl

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Yep. Differentiate it and see where the derivative doesn't exist.

Apr 17, 2005

quasar987

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You have to use the definition of the derivative (the limit).

Notice how limit from the right and limit from the left are different as x approaches -2 and +2 from both sides.

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