$$\[ y=\arccos (\operatorname{sech} x) \quad x> 0 \]$$ Figure 1 shows a sketch of part of the curve $$\(C\)$$ with equation $$\(y=\mathrm{f}(x)\)$$ where $$\[ \mathrm{f}(x)=\arccos (\operatorname{sech} x)+\operatorname{coth} x \quad x> 0 \]$$ The point $$\(P\)$$ is a minimum turning point of $$\(C\)$$ (b) Show that the $$\(x\)$$ coordinate of $$\(P\)$$ is $$\(\ln (q+\sqrt{q})\)$$ where $$\(q=\frac{1}{2}(1+\sqrt{k})\)$$ and $$\(k\)$$ is an integer to be determined. (6)

Answer:

Knowledge points:

Solution: