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Mathematics
Mathematics
Problem
Consider the function
q
(
x
)
=
sec
(
3
x
2
+
1
)
q(x)=\sec\!\bigl(\sqrt{3x^{2}+1}\bigr)
q
(
x
)
=
sec
(
3
x
2
+
1
)
. (a) Derive an expression for
q
′
(
x
)
q'(x)
q
′
(
x
)
in its simplest form. (b) Evaluate
q
′
(
2
)
q'(2)
q
′
(
2
)
, expressing your answer exactly. (c) Use the result from part (a) to explain whether
q
q
q
is increasing or decreasing at
x
=
2
x=2
x
=
2
.
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