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Can a function be differentiable at a point where the derivative is not defined?
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I recently came across the function f(x)=(1-x)sqrt(1-x^2) defined on [-1;1]. The function is only differentiable on ]-1;1[.
However, using the rate of change method, we find that f is differentiable for x=1 and has a horizontal tangent at that point (y=0).
I don't understand how a function can be differentiable at point on which the derivative is not defined. Could someone provide some explanation?
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