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Mathematics
Mathematics
Problem
Let
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
,
F(x)=\int_{0}^{x} f(t)\,dt,
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
,
where
f
(
t
)
=
{
t
2
,
t
<
2
,
5
,
t
≥
2.
f(t)=\begin{cases} t^{2}, & t<2,\\ 5, & t\ge 2. \end{cases}
f
(
t
)
=
{
t
2
,
5
,
t
<
2
,
t
≥
2.
Which of the following describes
F
′
(
x
)
F'(x)
F
′
(
x
)
at
x
=
2
x=2
x
=
2
? a)
F
′
(
2
)
=
5
F'(2)=5
F
′
(
2
)
=
5
b)
F
′
(
2
)
F'(2)
F
′
(
2
)
does not exist because
f
f
f
is not continuous at
t
=
2
t=2
t
=
2
. c)
F
′
(
2
)
=
4.5
F'(2)=4.5
F
′
(
2
)
=
4.5
d)
F
′
(
2
)
=
8
3
F'(2)=\dfrac{8}{3}
F
′
(
2
)
=
3
8
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