This week in class we have been learning about differentiability. This was a somewhat difficult to understand. We learned that taking a derivative is taking a slope of a function.
Differentiability
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
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