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Let f$($x$)=$ln$($x$+1)^(*)$cos$($x$)+($sin$($x$))/($x$+2)$ on $(-1,6].$

a$.$ On what interval$($s$)$ is f$($x$)$ increasing and concave down? Explain your reasoning. $(3$pts$)$

b$.$ Identify all points of inflection. Justify your answer. $(3$pts$)$