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Mathematics
Mathematics
Problem
Let
F
(
x
)
=
∫
1
x
(
t
3
−
2
t
+
1
)
d
t
F(x)=\displaystyle \int_{1}^{x}(t^{3}-2t+1)\,dt
F
(
x
)
=
∫
1
x
(
t
3
−
2
t
+
1
)
d
t
. (i) Find
F
′
(
x
)
F'(x)
F
′
(
x
)
. (ii) Evaluate
F
′
(
2
)
F'(2)
F
′
(
2
)
. (iii) Using the value of
F
′
(
1
)
F'(1)
F
′
(
1
)
, obtain the equation of the tangent to the curve
y
=
F
(
x
)
y=F(x)
y
=
F
(
x
)
at the point where
x
=
1
x=1
x
=
1
.
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