Question

Задания прикреплены ( решить нужно №183, 184 )

Answer 1

183.

a)$f(x)=x^3-3x^2+7x\f`(x)=3x^2-6x+7\f`(x)=0\3x^2-6x+7=0\D=(-6)^2-4*3*7=36-84=-48<0$

   решений нет

б)$f(x)=3x^3-2x^2-1\f`(x)=9x^2-4x=x(9x-4)\f`(x)=0\x(9x-4)=0$

 

   $x=0$      или            $9x-4=0$

                                                 $9x=4$

                                                 $x=4/9$

 

184.

$f(x)=frac{1}{3}x^3+4x^2-9x+1\f`(x)=x^2+8x-9\f`(x)>0\x^2+8x-9>0\(x+9)(x-1)>0$

 

                    +                                         -                                           +

____________ -9 ____________________ 1 _________________

 

$xin(-infty;-9)cup(1;+infty)$

 

 

 

$f(x)=-frac{1}{3}x^3+x^2+3x\f`(x)=-x^2+2x+3\f`(x)>0\-x^2+2x+3>0\x^2-2x-3<0\(x+1)(x-3)<0$

 

 

                     +                                        _                                         +

________________ -1 _______________ 3 _____________________

 

$xin(-1;3)$