Контрольная работа «Производная»

Вариант 1
Часть А
А1. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) 12х2 2) 12х 3) 4х2 4) 12х3
А2. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) –5 2) 11 3) 6 4) 6х
А3. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) HYPER13 EMBED Equation.3 HYPER14HYPER15 2) HYPER13 EMBED Equation.3 HYPER14HYPER15 3) HYPER13 EMBED Equation.3 HYPER14HYPER15 4) HYPER13 EMBED Equation.3 HYPER14HYPER15
А4. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) HYPER13 EMBED Equation.3 HYPER14HYPER15 2) HYPER13 EMBED Equation.3 HYPER14HYPER15 3) HYPER13 EMBED Equation.3 HYPER14HYPER15 4) HYPER13 EMBED Equation.3 HYPER14HYPER15
А5. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) HYPER13 EMBED Equation.3 HYPER14HYPER15 2) HYPER13 EMBED Equation.3 HYPER14HYPER15 3) HYPER13 EMBED Equation.3 HYPER14HYPER15 4) HYPER13 EMBED Equation.3 HYPER14HYPER15
А6. Найдите производную функции HYPER13 EMBED Equation.DSMT4 HYPER14HYPER15.
HYPER13 EMBED Equation.3 HYPER14HYPER15
А7. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) HYPER13 EMBED Equation.3 HYPER14HYPER15 2) HYPER13 EMBED Equation.3 HYPER14HYPER15 3) HYPER13 EMBED Equation.3 HYPER14HYPER15 4) HYPER13 EMBED Equation.3 HYPER14HYPER15
А8. Найдите производную функции HYPER13 EMBED Equation.DSMT4 HYPER14HYPER15
1) HYPER13 EMBED Equation.DSMT4 HYPER14HYPER15 2) HYPER13 EMBED Equation.DSMT4 HYPER14HYPER15 3) HYPER13 EMBED Equation.DSMT4 HYPER14HYPER15 4) HYPER13 EMBED Equation.DSMT4 HYPER14HYPER15
А9. Вычислите значение производной функции HYPER13 EMBED Equation.3 HYPER14HYPER15
в точке HYPER13 EMBED Equation.3 HYPER14HYPER15 . 1) 2 2) HYPER13 EMBED Equation.3 HYPER14HYPER15 3) 0,5 4) HYPER13 EMBED Equation.3 HYPER14HYPER15
А10. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) HYPER13 EMBED Equation.3 HYPER14HYPER15 2) HYPER13 EMBED Equation.3 HYPER14HYPER15 3) HYPER13 EMBED Equation.3 HYPER14HYPER15 4) HYPER13 EMBED Equation.3 HYPER14HYPER15

Часть В
1. Найдите производную функции: а) f(x)= xHYPER13 EMBED Equation.3 HYPER14HYPER15– 3xHYPER13 EMBED Equation.3 HYPER14HYPER15– HYPER13 EMBED Equation.3 HYPER14HYPER15 + 2; б) f(x)= HYPER13 EMBED Equation.3 HYPER14HYPER15.
2. Вычислите производную функции f(x)= (х + 1)HYPER13 EMBED Equation.3 HYPER14HYPER15 в точках 2; 4; х; х – 2.
3. Решите неравенство f(x)
· 0, если f(x)= 3х – хHYPER13 EMBED Equation.3 HYPER14HYPER15.
4. Найдите производную функции f(x)= HYPER13 EMBED Equation.3 HYPER14HYPER15 в точках х и tHYPER13 EMBED Equation.3 HYPER14HYPER15.
5. Найдите тангенс угла наклона касательной к графику функции HYPER13 QUOTE HYPER14HYPER15в точке х0:
а) HYPER13 QUOTE HYPER14HYPER15, х0 = – 1; б) HYPER13 QUOTE HYPER14HYPER15, х0 = HYPER13 QUOTE HYPER14HYPER15.
6. Составьте уравнение касательной к графику функции HYPER13 QUOTE HYPER14HYPER15в точке M:
а) HYPER13 QUOTE HYPER14HYPER15, M(–3;9); б) HYPER13 QUOTE HYPER14HYPER15, M(2;3).
7. Вычислите значение производной функции HYPER13 EMBED Equation.3 HYPER14HYPER15 в точке хо= 26.
8. Найдите значение х, при которых производная функции HYPER13 EMBED Equation.3 HYPER14HYPER15 равна 0.

Вариант 2
Часть А
А1. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) HYPER13 EMBED Equation.3 HYPER14HYPER15 2) HYPER13 EMBED Equatio
·n.3 HYPER14HYPER15 3) 18 x5 4) HYPER13 EMBED Equation.3 HYPER14HYPER15
А2. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) 7 2) 12 3) –5 4) –5х
А3. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) HYPER13 EMBED Equation.3 HYPER14HYPER15 2) HYPER13 EMBED Equation.3 HYPER14HYPER15 3) HYPER13 EMBED Equation.3 HYPER14HYPER15 4) HYPER13 EMBED Equation.3 HYPER14HYPER15
А4. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) HYPER13 EMBED Equation.3 HYPER14HYPER15 2) HYPER13 EMBED Equation.3 HYPER14HYPER15 3) HYPER13 EMBED Equation.3 HYPER14HYPER15 4) HYPER13 EMBED Equation.3 HYPER14HYPER15
А5. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) HYPER13 EMBED Equation.3 HYPER14HYPER15 2) HYPER13 EMBED Equation.3 HYPER14HYPER15 3) HYPER13 EMBED Equation.3 HYPER14HYPER15 4) HYPER13 EMBED Equation.3 HYPER14HYPER15
А6. Вычислите значение производной функции HYPER13 EMBED Equation.3 HYPER14HYPER15 в точке хо=2.
1) 13 2) - 3 3) 8 4) 27
А7. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) HYPER13 EMBED Equation.3 HYPER14HYPER15 2) HYPER13 EMBED Equation.3 HYPER14HYPER15 3) HYPER13 EMBED Equation.3 HYPER14HYPER15 4) HYPER13 EMBED Equation.3 HYPER14HYPER15
А8. Вычислите значение производной функции HYPER13 EMBED Equation.3 HYPER14HYPER15 в точке HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) –47 2) –49 3) 47 4) 11,5
А9. Вычислите значение производной функции HYPER13 EMBED Equation.3 HYPER14HYPER15
в точке HYPER13 EMBED Equation.3 HYPER14HYPER15 . 1) 2 2) –1 3) –2 4) HYPER13 EMBED Equation.3 HYPER14HYPER15
А10. Найдите производную функции HYPER13 EMBED Equation.3 HYPER14HYPER15.
1) HYPER13 EMBED Equation.3 HYPER14HYPER15 2) HYPER13 EMBED Equation.3 HYPER14HYPER15 3) HYPER13 EMBED Equation.3 HYPER14HYPER15 4) HYPER13 EMBED Equation.3 HYPER14HYPER15
Часть В
1. Найдите производную функции: а) f(x)= xHYPER13 EMBED Equation.3 HYPER14HYPER15+ 2xHYPER13 EMBED Equation.3 HYPER14HYPER15– HYPER13 EMBED Equation.3 HYPER14HYPER15 – 1; б) f(x)=HYPER13 EMBED Equation.3 HYPER14HYPER15.
2. Вычислите производную функции f(x)= х HYPER13 EMBED Equation.3 HYPER14HYPER15 в точках 0; 3; х; х – 1.
3. Решите неравенство f(x) < 0, если f(x)= х – 3хHYPER13 EMBED Equation.3 HYPER14HYPER15
4. Найдите производную функции f(x)= HYPER13 EMBED Equation.3 HYPER14HYPER15в точках х и tHYPER13 EMBED Equation.3 HYPER14HYPER15.
5. Найдите тангенс угла наклона касательной к графику функции HYPER13 QUOTE HYPER14HYPER15в точке х0:
а) HYPER13 QUOTE HYPER14HYPER15, х0 = – 3; б) HYPER13 QUOTE HYPER14HYPER15, х0 =HYPER13 QUOTE HYPER14HYPER15.
6. Составьте уравнение касательной к графику функции HYPER13 QUOTE HYPER14HYPER15в точке M:
а) HYPER13 QUOTE HYPER14HYPER15, M(3;9); б) HYPER13 QUOTE HYPER14HYPER15, M(–2;3).
7. Вычислите значение производной функции HYPER13 EMBED Equation.3 HYPER14HYPER15 в точке хо= –7.
8. Найдите значение х, при которых производная функции HYPER13 EMBED Equation.3 HYPER14HYPER15 равна 0.

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