Ally makes $15 per hour. She works 40 hours a week. How much money will Ally make in February? Hint: February has 28 days.
2 answers:
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Answer:
Step-by-step explanation:
Let's get all of the terms with the on the right-hand side of the equation, and everything else on the left-hand side of the equation.
To do this, we should add to both sides of the equation to remove the
from the left-hand side of the equation:
Finally, to get the by itself, we can divide both sides by
:
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.