2. A function is defined by: $$f ( x ) = \sqrt { \frac { 1 - x } { 1 + x } } , x \in \mathbb { R } , | x | < 1$$ a) P and Q are points on the curve with \(x\)-coordinates \(x\) and \(x + h\) respectively. Find the gradient of the line segment PQ . Simplify your answer to a single fraction.
b) Use differentiation from first principles to show that: $$f ^ { \prime } ( x ) = - \frac { 1 } { ( 1 + x ) \sqrt { 1 - x ^ { 2 } } }$$ c) Sketch the curve on the axes provided over the page, showing clearly the behaviour of the curve near \(x = 0\) and \(x = \pm 1\).
[0pt] [Question 2 - Continued]
[0pt] [Question 2 - Continued]
[0pt] [Question 2 - Continued]
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