Найти точку минимума функции y=4х-4ln(х+7)

Решите задачу:

$y=4x-4ln(x+7) \\ \\ x+7\ \textgreater \ 0\rightarrow x\ \textgreater \ -7 \\ \\ y'=4- \frac{4}{x+7} \\ y'= \frac{4x+28-4}{x+7} = \frac{4x+24}{x+7} \\ y'\ \textgreater \ 0\iff \frac{4x+24}{x+7}\ \textgreater \ 0\iff x\in (-\infty;-7)\vee (-6;\infty) \\ y'\ \textless \ 0\iff \frac{4x+24}{x+7}\ \textless \ 0\iff x\in (-7;-6) \\ x=-6\rightarrow y_{MIN} \\ y(-6)=4*(-6)-4ln(-6+7)=-24-4ln1=-24-0=-24 \\ MIN(-6;-24) \\$