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Mathematics
Mathematics
Problem
Consider the function
F
(
x
)
=
x
4
−
4
x
3
+
x
2
+
2
sin
x
−
3
cos
x
F(x)=x^{4}-4x^{3}+x^{2}+2\sin x-3\cos x
F
(
x
)
=
x
4
−
4
x
3
+
x
2
+
2
sin
x
−
3
cos
x
. a. (i) Differentiate
F
(
x
)
F(x)
F
(
x
)
with respect to
x
x
x
and simplify the result. b. (ii) Factorise completely the polynomial part of
F
′
(
x
)
F'(x)
F
′
(
x
)
. c. (iii) Evaluate
F
′
(
π
2
)
F'\!\left(\dfrac{\pi}{2}\right)
F
′
(
2
π
)
, writing your answer in exact form.
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