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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
(
2
x
+
5
)
tan
3
x
f(x)=\bigl(2x+5\bigr)\tan 3x
f
(
x
)
=
(
2
x
+
5
)
tan
3
x
. Answer the following: a. (i) Find
f
′
(
x
)
f'(x)
f
′
(
x
)
. b. (ii) Evaluate
f
′
(
π
6
)
f'\bigl(\tfrac{\pi}{6}\bigr)
f
′
(
6
π
)
. c. (iii) Show that
f
′
(
x
+
π
)
=
f
′
(
x
)
f'(x+\pi)=f'(x)
f
′
(
x
+
π
)
=
f
′
(
x
)
for all real
x
x
x
. What does this tell you about the period of
f
′
(
x
)
f'(x)
f
′
(
x
)
?
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