本题目来源于试卷: Differential Calculus，类别为 IB数学
[问答题]
Consider the function defcybv,zn,, 56iip,v ,llb x-ei*hu*e:6mevype8 1 ac t)6dyhfined by $ f(x)=(2 x-6) \ln (x+3)+x $ for $x \in \mathbb{R}$, $x\lt p$ .
1. Find the value of p .
2. Find an expression for $f^{\prime}(x)$ .
The graph of y=f(x) has no points of inflexion.
3. Determine if the graph of y=f(x) is concave down or concave up over its domain.
The function g is defined by g(x)=3$\ln \left(\frac{1}{x+3}\right)+x$ , for $x \in \mathbb{R}$, $x\lt -3$ .
4. Find an expression for $g^{\prime}(x)$ .
5. Find the horizontal and vertical asymptotes of $g^{\prime}(x)$ .
6 . Find the exact value of the minimum of y=g(x) .
7. Solve $f(x)\lt g(x)$ for $x \in \mathbb{R}, x\lt -3$ .
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