when you are comparing 1/2 to 3/6. this is because you know that 1/2 is equal to 3/6. You are very welcome, and thank you for the challenge.
By definition of absolute value, you have

or more simply,

On their own, each piece is differentiable over their respective domains, except at the point where they split off.
For <em>x</em> > -1, we have
(<em>x</em> + 1)<em>'</em> = 1
while for <em>x</em> < -1,
(-<em>x</em> - 1)<em>'</em> = -1
More concisely,

Note the strict inequalities in the definition of <em>f '(x)</em>.
In order for <em>f(x)</em> to be differentiable at <em>x</em> = -1, the derivative <em>f '(x)</em> must be continuous at <em>x</em> = -1. But this is not the case, because the limits from either side of <em>x</em> = -1 for the derivative do not match:


All this to say that <em>f(x)</em> is differentiable everywhere on its domain, <em>except</em> at the point <em>x</em> = -1.
Answer:
16 year olds had the higher ratio of black belts to brown belts.
Step-by-step explanation:
15 year olds: 8/28 students had black belts
8/28 = 28.6% had black belts
16 year olds: 10/27 students had bald belts
10/27 = 37.0% had black belts
This is a 90-60-30 triangle so the angle is 30 degrees.