For $x > -1$, the function $f$ is given by $f(x) = 2x + (x + 1)^{-2}$.
(a)[4]
Find $f'(x)$ and $f''(x)$ and hence confirm that $f$ has a minimum value when $x = 0$.
(b)[2]
The points $A\left(-\frac{1}{2}, 3\right)$ and $B\left(1, 2\frac{1}{4}\right)$ are on the curve $y = 2x + (x + 1)^{-2}$. Find the distance $AB$.
(c)[6]
Show all necessary working and find the area of the shaded region.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate to obtain $f'(x)=2-2(x+1)^{-3}$.” …
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