Question

найдите точку максимума функции y=ln(x+13)-4x+8

Answer 1

$y=ln(x+13)-4x+8\\y`=frac{(x+13)`}{x+13}-4=frac{1}{x+13}-frac{4x+52}{x+13}=\\=frac{1-4x-52}{x+13}=frac{-4x-51}{x+13}=-frac{4(x+12,75}{x+13}\\y`(x)=0\\-frac{4(x+12,75)}{x+13}=0$
                
                      -                     +                              -
_______________-13___________-12,75___________
                               min                       max
x(max)=-12,75

Answer 2

у`=1/(х+13)-4 ; приравниваем к 0, получаем х=-13+1/4=-12,25