at our lessons we answer the teacher's questions.
in england they don't go to school every day.
i do my homework in my bedroom.
the pupils on duty tidy the classroom.
all the pupils have to wear uniforms.
i come to school at a quarter to eight.
we like to make reports.
i do me homework every day.
i have my music lessons two times a week.
we have english three times a week.
this magazine is published to times a month.
i visit my aunt three times a month.
i never miss classes.
i go to the forest very often.
they seldom go to the theatre.
i don't want to answer the teacher's questions.
my friends and i go to school every day.
i do my homework at school.
every friday the students tidy their classrooms.
we don't have to wear a uniform at our school.
as a rule they come to school at 8 a.m.
my sister like to make reports on geography.
we must do washing up every day.
i have to play chess two times a week.
we go to a swimming pool three times a week.
my mother goes to the dentist two times a month.
i go to the disco three times a month.
i have never been to volgograd.
she goes to the cinema very often.
they seldom sing and dance.
1) D(y)=(-∞;+∞)
2) f(-x)=2(-x)^3 +3(-x)^2 -1=-2x^3-3x^2-1=-(2x^3 +3x^2 +1)≠f(x)
нечетная функция;
3)Точки пересечения графика с осями координат:
с осью у: х=0; f(0)=-1 (0;-1)
с осью у: у=0; 2x^3+3x^2 -1=0; 2x^3 +2x^2 +x^2-1=0;
2x^2 *(x+1) +(x-1)(x+1)=0
(x+1)(2x^2 +x-1)=0
x+1=0 ili 2x^2+x-1=0
x=-1 D=1+8=9=3^2
x1=(-1-3)/4=-1; x2=1/2=0,5
(-1;0); (0,5;0)
4) Возрастание(убывание)
f'(x)=(2x^3 +3x^2 -1)'=6x^2+6x;
f'(x)=0; 6x^2+6x=0; 6x(x+1)=0; x=0 ili x+1=0
x=-1
f'(x) + - +
(-1)0>x
f(x) возрастает убывает возрастает
max min
f(-1)=2(-1)^3 +3(-1)^2 -1=-2+3-1=0 -максимум функции
f(0)=-1 минимум ф-и; В точках (0;-1) и(-1;0) будет перегиб(как парабола)
5) Для точности построения графика функции зададим таблицу:
x | -2 | -0,5 | 1 | f(-2)=2*(-2)^3+3*(-2)^2-1=-16+12-1=-5
y | -5 | -0,5 | 4 | а также точки (0;-1); (-1;0); (0,5;0)
6) Строим график по найденным точкам.