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:
Step-by-step explanation:
Answer:
10=19-11
Step-by-step explanation:
that answer is false because 19-11 = 8 not 10
Answer:
Adult Ticket Price = $13
Child Ticket Price = $13
Step-by-step explanation:
Let price of adult ticket be "a" and child ticket be "c"
13 adult and 14 child equals $351, so we can write:
13a + 14c = 351
and
2 adult and 7 child equals $117, thus we can write:
2a + 7c = 117
We multiply 2nd equation by (-2) to get:
-2 * [2a + 7c = 117]
= -4a -14c = -234
Adding botht he "bold" equations, we get:
13a + 14c = 351
-4a -14c = -234
------------------------
9a = 117
a = 117/9 = 13
Now to find b, we use the value of a gotten in the first equation:
13a + 14c = 351
13(13) + 14c = 351
169 + 14c = 351
14c = 182
c = 182/14 = 13
Hence,
<em>Adult Ticket Price = $13</em>
<em>Child Ticket Price = $13</em>
