Is a function differentiable at all points that it is continuous?
1 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.