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Mathematics
Mathematics
Problem
Consider
h
(
x
)
=
4
cot
x
−
2
ln
x
+
6
cos
x
h(x)=4\cot x-2\ln x+6\cos x
h
(
x
)
=
4
cot
x
−
2
ln
x
+
6
cos
x
. (i) Differentiate
h
(
x
)
h(x)
h
(
x
)
with respect to
x
x
x
. (ii) Show that
h
′
(
x
)
=
−
4
csc
2
x
−
2
x
−
6
sin
x
h'(x)=-4\csc^{2}x-\dfrac{2}{x}-6\sin x
h
′
(
x
)
=
−
4
csc
2
x
−
x
2
−
6
sin
x
. (iii) Find all values of
x
x
x
in
(
0
,
π
)
(0,\pi)
(
0
,
π
)
for which
h
′
(
x
)
=
0
h'(x)=0
h
′
(
x
)
=
0
.
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