Question 12 - A-Level Maths

Show that the equation $$2 \cot ^ { 2 } x + 2 \operatorname { cosec } ^ { 2 } x = 1 + 4 \operatorname { cosec } x$$ can be written in the form $$a \operatorname { cosec } ^ { 2 } x + b \operatorname { cosec } x + c = 0$$ 12
Hence, given $x$ is obtuse and $$2 \cot ^ { 2 } x + 2 \operatorname { cosec } ^ { 2 } x = 1 + 4 \operatorname { cosec } x$$ find the exact value of $\tan x$ Fully justify your answer.

13 A curve, $C$, has equation
$y = \frac { \mathrm { e } ^ { 3 x - 5 } } { x ^ { 2 } }$
Show that $C$ has exactly one stationary point.
Fully justify your answer.

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13	A curve, \(C\), has equation
	\(y = \frac { \mathrm { e } ^ { 3 x - 5 } } { x ^ { 2 } }\)

	Show that \(C\) has exactly one stationary point.

	Fully justify your answer.