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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
3
sin
x
−
4
cos
x
f(x)=3\sin x-4\cos x
f
(
x
)
=
3
sin
x
−
4
cos
x
. (i) Find
f
′
(
x
)
f'(x)
f
′
(
x
)
. (ii) Calculate
f
′
(
π
4
)
f'\!\left(\dfrac{\pi}{4}\right)
f
′
(
4
π
)
, giving your answer in simplest form. (iii) Determine all values of
x
x
x
in the interval
[
0
,
2
π
]
[0,2\pi]
[
0
,
2
π
]
for which
f
′
(
x
)
=
0
f'(x)=0
f
′
(
x
)
=
0
.
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