Differentiability
Published in
1 min readJan 23, 2019
“If the point of a function IS differentiable, then it MUST BE continuous at the point.”
Example of NOT differentiable
points:
You can see, if the point DOES NOT have limit
, it's NOT DIFFERENTIABLE.
In another word, the point is not CONTINUOUS, it's Jump Discontinuity
, or Removable Discontinuity
, or any type of discontinuities.
Not differentiable situations
- Vertical Tangent (∞)
- Not Continuous
- Two sides’ limits are different
Vertical Tangent
We know that the Slope of Vertical Tangent
is UNDEFINED,
on the contrary:
IT IS A VERTICAL TANGENT, IF:
- The derivative
dy/dx = undefined
, or - The
denominator of derivative's expression = 0
.
Horizontal Tangent
It’s a Horizontal Tangent, if:
dy/dx = 0
.