Найдите точки, в которых касательные к кривым f(x)=x^3−x−1 и g(x)=3x^2−4x+1 параллельны. написать уравнения этих касательных

Находим производные: f'(x)=3x^2-1, g'(x)=6x-4.
Значение производной в точке касания определяет угловой коэффициент касательной в этой точке. Поскольку касательные параллельны, то производные можно приравнять (у касательных равны угловые коэффициенты), поэтому 3x^2-1=6x-4<=>3x^2-6x+3=0<=>x^2-2x+1=0=>
=>x1=1,x2=1. f(1)=1^3-1-1=-1, g(1)=3*1^2-4*1+1=0. f'(1)=2, g'(1)=2.
Составляем уравнения касательных: f(x)=>y+1=2(x-1), y=2x-3,
g(x)=>y-0=2(x-1), y=2x-2. Ну, и для наглядности графики

1  yesterday i had  breakfast at the canteen.  2  last summer we went to the black sea.  3  he didn't call  me last week.  4  why did this girl come to  our office yesterday?   5  when did  you buy tickets last time?   6  last june the boys played  football every morning.  7  on sunday my parents  were at the theatre.  8  i didn't take part at the conference last month.  9  he lived in kiev in his childhood.  10  where did  he send his message?   2 трансформируйте предложения в past simplе  1  he often played chess.  2  our classes began at 9 a. m.  3  she  was always busy.  4  what did you do in the evening?   5  my sister didn’t study at school, she worked at the hospital. 6  my friend prefered tea to coffee.  7  i found many stories in this magazine.  8  he was in my room,  wasn't he?   9  why did you always ask so many questions?   10  jasmine seldom visited her grandparents. 3 образуйте отрицательную форму предложений  1  in summer she didn't get up early.  2  mr. white  didn't write a lot of letters yesterday.  3  on friday they weren't at the station.  4  we didn't  enjoy our time in rome.  5  they didn't  watch a football match last weekend.  6  the girl didn't open a box at once.  7  i didn't leave my keys on the table.  8  the engineer didn't go on business trip on monday.  9  my friend didn't want to move to another flat.  10  i didn't find a surprise in the present-box. 4 поставьте вопросы к предложениям.  1  he learned english at school. (where? what language? why? or …? )  where did he learn english? what language did he learn? why did he learn english? did he learn english or french? 2  the train was five hours late. (what? why? )  what was 5 hours late? why was the train five hours late? 3  i was going to stay at my aunt’s in the crimea. (where? who? or …? ) where was i going to stay in the crimea? who was going to stay at the aunt's in the crimea? was i going to stay at my aunt's or in the hotel in the crimea?   4  they stayed in moscow only for two days. (why? where? how long? ) why did they stay in m only for 2 days? where did they stay? how long did they stay in m?   5  i bought a very beautiful dress in this shop last weekend. (where? what? when? ) where did i buy a very beautiful dress last weekend? what did i buy in this shop last weekend? when did i buy this beautiful dress in the shop? 6  they traveled to cyprus by sea. (how? where? or …? ) how did they travel to c? where did they travel to? did they travel to c or ibiza?   7  i didn’t find your telephone number. (what? why? )  what didn't i find? why didn't i find your telephone number? 8  in his childhood he was always a leader among his friends. (what? when? who? )  what was he in his childhood? when was he a leader among his friends? who was always a leader among his friends in his childhood? 9  he caught a cold last month. (what? when? why? ) what did he catch? when did he catch a cold? why did he catch a cold?   10  we did our lessons together. (what? how? ) what did we do together? how did we do our lessons?

Пусть х(км/ч)-собственная скорость катера, а у(км/ч)-скорость течения реки, тогда скорость катера по течению равна (х+у)км/ч, а против течения (х-у)км/ч). Путь пройденный катером по течению равен 1,5(х+у)км., а путь против течения равен 9/4(х-у)км. (9/4ч-это 2ч15мин)
. Составим и решим систему уравнений:
1,5(х+у)=27,умножаем на 10
9/4(х-у)=27;умножаем на 4
 15(х+у)=270,
9(х-у)=108; 

15х+15у=270,разделим на 5 и умножим на 3

 9х-9у=162,
9х-9у=108;
решаем сложения:
 18х=270,
9х-9у=108; 

х=15,
9*15-9у=108;

 х=15,
-9у=-27;

 х=15,
у=3. 
15(км/ч)-собственная скорость катера
3(км/ч)-скорость течения реки