Blog for 1/16

Well, this week we learned a little bit more about derivatives.....sadly, I still can't do them too well......so I think I'll just talk about stuff being differentiable.......

differentiability is the ability to take a derivative from a function

there are many ways that a function cannot be differentiable
those ways are:

1) if there is a curve
curves occur when absolute values and/or piecewises are found in the function that you are trying to take the derivative of
an example of a function with a curve is:
1) |3-x| you set what's inside of the absolute value equal to 0 and solve for x, so |3-x| is not differentiable at x=3

2) if there is a vertical asymptote
vertical asymptotes occur when x is raised to the (odd/odd)
x^5/9 would be a vertical asymptote, so x would not be differentiable at x=1

3) if it's not continuous
if a function is not continuous, then it's not differentiable, it's as simple as that

4) if there's a cusp
a cusp is when you have x^(even/odd)
x^2/7 would not be differentiable at x=0