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Is the above function differentiable for all values of x? Why?

Is the above function differentiable for all values of x? Why?-example-1

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No, the function has a sharp turn on the first quadrant so it is not differentiable.Yellow

What is a continuous function curve?

A continuous function curve has no breaks, holes, or jumps. It is a smooth, connected line without interruptions, indicating a continuous relationship between input and output values.

From the given curve

The curve is not connected in its entire curve. it has sharp turn in the first quadrant which represents sudden jump along its curve.

Therefore, the function is discontinuous.

This implies that

lim => a f(x) = lim => a f(x) ≠ f(a)

A discontinuous function is not differentiable.

Therefore, no, the function has a sharp turn on the first quadrant so it is not differentiable. Yellow

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