Question

What is differentiability. Give examples.

Answer 1

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==> A function is differentiable at a point when there's a defined derivative at that point. This means that the slope of the tangent line of the points from the left is approaching the same value as the slope of the tangent of the points from the right.

Example: is x2 + 6x differentiable? Derivative rules tell us the derivative of x2 is 2x and the derivative of x is 1, so: Its derivative is 2x + 6. So yes! x2 + 6x is differentiable.

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Answer 2

Explanation:

differentiable function of one real variable is a function whose derivative exists at each point in its domain. As a result, the graph of a differentiable function must have a (non-vertical) tangent line at each interior point in its domain, be relatively smooth, and cannot contain any break, angle, or cusp.