The rules of differentiation tell us that the derivative of \(x^3\) is \(3x^2\), the derivative of \(x^2\) is \(2x\), and the derivative So, the derivative of \(f\) is \(f'(x) = 3x^2 + 6x + 2\). This derivative exists for every possible value of \(x\)! we can

Presumably, you have been given a function defined piecewise over an interval, and you want to know whether the function is differentiable at the edges where the pieces meet. Suppose the

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If the function is undefined or does not exist at a point, then we say that the function is discontinuous. Definition of Differentiability : f ( x) is said to be differentiable at the point x = a

The function is differentiable from the left and right. As in the case of the existence of limits of a function at x 0, it follows that exists if and only if both exist and f' (x 0 -) = f' (x 0 +) Hence if and only if f' (x 0 -) = f' (x 0 +) . If any one

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What is Differentiable? A function is said to be differentiable if the derivative of the function exists at all points in its domain. Particularly, if a function f (x) is differentiable at x = a, then f′ (a) exists in the domain. Let us look at some