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Mathematics
Mathematics
Problem
The function
p
(
x
)
=
x
p(x)=\sqrt{x}
p
(
x
)
=
x
is defined on the interval
[
0
,
4
]
[0,4]
[
0
,
4
]
. Which of the following describes
p
′
(
0
)
p'(0)
p
′
(
0
)
? a)
p
′
(
0
)
=
0
p'(0)=0
p
′
(
0
)
=
0
b)
p
′
(
0
)
p'(0)
p
′
(
0
)
does not exist because
lim
x
→
0
+
x
−
0
x
−
0
\displaystyle \lim_{x\to 0^{+}} \dfrac{\sqrt{x}-0}{x-0}
x
→
0
+
lim
x
−
0
x
−
0
is unbounded. c)
p
′
(
0
)
=
∞
p'(0)=\infty
p
′
(
0
)
=
∞
d)
p
′
(
0
)
p'(0)
p
′
(
0
)
does not exist because
p
p
p
is not defined for
x
<
0
x<0
x
<
0
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