本题目来源于试卷: Modulus & Inequalities，类别为 IB数学
[问答题]
Consider the functioz5 9yv/n+ m50tk+6;2 d4trc of;zjzinlcva vmn yylqjc p8y:i 0n 1-l:)zcyn o6defined by $f(x)=(2 x-6) \ln (x+3)+x $ for $ x \in \mathbb{R}$, x>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>-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)-3 .
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