How to know if a function is differentiable on an interval

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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Differentiable

A function f (x) is differentiable at the point x = a if the following limit exists: Example: Consider the absolute value function given by f (x) = |x|. We will determine if this function is differentiable at c = 0 or not. Let's find the limit lim

Continuity and Differentiability (Fully Explained w/ Examples!)

A function is differentiable at a point when it is both continuous at the point and doesn’t have a “cusp”. A cusp shows up if the slope of the function suddenly changes. An example of this can

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The function f is differentiable at x if lim

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Prove whether the function is differentiable about a given

Check if Differentiable Over an Interval. f (x) = 4x − 2 f ( x) = 4 x - 2 , (1,3) ( 1, 3) Find the derivative. Tap for more steps 4 4. Find if the derivative is continuous on (1,3) ( 1, 3). Tap for more

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