Question 2 - A-Level Maths

Exam Board	SPS
Module	SPS FM Pure (SPS FM Pure)
Year	2020
Session	February
Topic	Taylor series
Type	Inverse functions (inverse trig/hyperbolic)

Given that $$f ( x ) = \tan ^ { - 1 } ( x + 1 )$$ find $f ( 0 )$ and $f ^ { \prime } ( 0 )$, and show that $f ^ { \prime \prime } ( 0 ) = - \frac { 1 } { 2 }$.
Hence find the first three terms in the Maclaurin series for $f ( x )$