Blog 3

Chapter two deals with derivatives being differentiable. There are three ways a function is not differentiable. A function is not differentiable if:

1. There is a corner (there is a corner if there is an absolute value or a piecewise)

2. Vertical tangent line

-the exponent is x=^odd/odd

3. If it is not continuous it is either a jump, removable, vertical asymptotes

4. Also, if there is a cusp.

-A cusp is when x=even/odd. When graphing a function a cusp will show up as a dip in the graph.

*Sin x is differentiable, and sin absolute value of x has a corner.

Ex: Where is |x+2| not differentiable?

-Set what is inside equal to 0. X is differentiable at x=-2

Ex: Where is (x+3)^3/7 not differentiable?

-Notice that the exponent is x^odd/odd which makes it a vertical tangent line. The answer would be x=-3

If it asks you to describe the x-values at which f is differentiable you would graph it, and from there remember the rules that make functions differentiable. The answers often are infinity and negative infinity.

Source: Notes:)