Question

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

Answer 1

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