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**Differentiability and Piecewise Functions**

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**What are the three things that make a function not differentiable ?**

Not continuous at the point Vertical tangent line at the point A cusp at the point.

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**Where is the derivative undefined?**

1. …at a point of discontinuity. Example: f(x) is not differentiable at x = ____

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**Where is the derivative undefined?**

2. …where there is a vertical tangent line. Example: y = x1/3 is not differentiable at x = ___

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**3. …if the graph has a sharp point (cusp)**

Where is the derivative undefined? 3. …if the graph has a sharp point (cusp) f(x) is not differentiable at x = ____ f(x) is not differentiable at x = ____

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**Determine the value(s) of x at which the function is not differentiable. Give the reason.**

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**Derivatives of piecewise functions…**

If then, f ’(x)= f ’(5)= f ’(-2)=

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**Is the function continuous? Justify your answer.**

Is the function differentiable at x = 1? Justify your answer.

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**Determine whether the function is differentiable at x = 3**

Determine whether the function is differentiable at x = 3. Justify your answer.

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**Derivatives of Absolute value functions…**

If then, f ’(x)= f ’(5)= f ’(-2)=

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**Is the function differentiable everywhere?**

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