Devin's Blog

A function is not differentiable if:
1. There is a corner
a. Absolute value or a piecewise

2. Vertical tangent line
a. X^odd/odd

3. If it is not continuous
a. Jumps

b. Removables
c. Vertical asymptotes

4. There is a cusp
a. X^even/odd

Examples:
a. x+2/(X^2)
=there is a corner

b. X^5/3/(x)
=there is a vertical tangent line

c. X+1/x+1
=the function is not continuous

d. X^4/3/(x)
=there is a cusp

-If a function is not differentiable at a point you can take a derivative, but you cannot plug in “x”.
Using the steps and skills above you can educationally answer the following questions.
If a function is differentiable, is it continuous?
Yes
If a function is not differentiable, is it continuous?
Sometimes
If something is not differentiable, does it have a tangent line at that point?
No