# Is a function differentiable at all points that it is continuous?

##### 1 Answer

#### Answer:

No. Here are 3 examples.

#### Explanation:

**Example 1**

(The left and right derivatives are not equal -- there is no tangent line.)

graph{y=absx [-2.75, 2.724, -0.876, 1.862]}

**Example 2**

(

(

graph{root(3)x [-1.596, 1.441, -0.964, 0.555]}

**Example 3**

(

(

graph{x^(2/3) [-1.82, 1.597, -0.343, 1.366]}

I like this third example because it is also an example of a function whose minimum occurs at a critical point at which the derivative does not exist.