Home
Class 12
MATHS
f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f...

`f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3)" for all "x in R.`
The value of f(1) is

A

2

B

3

C

-1

D

4

Text Solution

AI Generated Solution

To find the value of \( f(1) \) for the function defined by \[ f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3) \] we will follow these steps: ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Matrix Match Type|6 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Numerical Value Type|45 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|29 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

  • DOT PRODUCT

    CENGAGE ENGLISH|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3)" for all "x in R. The value of f'(1)+f''(2)+f'''(3) is

f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3)" for all "x in R. f(x) is

Let f : RtoR be a function such that f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3),x in R . Then f(2) equals

f(x)=x^(2)+xg'(1)+g''(2)and g(x)=f(1)x^(2)+xf'(x)+f'(x). The value of f(3) is

Let f(x)=3x^(2)+4xg'(1)+g''(2) and, g(x)=2x^(2)+3xf'(2)+f''(3)" for all "x in R. Then,

Let g(x) =f(x)-2{f(x)}^2+9{f(x)}^3 for all x in R Then

If f(sinx)-f(-sinx)=x^(2)-1 is defined for all x in R , then the value of x^(2)-2 can be

If f(x) = (x + 1)/(x-1) , then the value of f{f(3)} is :

If f:R rarr R satisfying f(x-f(y))=f(f(y))+xf(y)+f(x)-1, for all x,y in R , then (-f(10))/7 is ……… .

Let f be a real valued function such that f(x)+3xf(1/x)=2(x+1) for all real x > 0. The value of f(5) is

CENGAGE ENGLISH-DIFFERENTIATION-Linked Comprehension Type
  1. f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x...

    Text Solution

    |

  2. f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x...

    Text Solution

    |

  3. f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3)" for all "x in R. The...

    Text Solution

    |

  4. f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3)" for all "x in R. f(x...

    Text Solution

    |

  5. f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3)" for all "x in R. The...

    Text Solution

    |

  6. Repeated roots : If equation f(x) = 0, where f(x) is a polyno- mial fu...

    Text Solution

    |

  7. Repeated roots : If equation f(x) = 0, where f(x) is a polyno- mial fu...

    Text Solution

    |

  8. Repeated roots : If equation f(x) = 0, where f(x) is a polyno- mial fu...

    Text Solution

    |

  9. Equation x^(n)-1=0, ngt1, n in N," has roots "1,a(1),a(2),…,a(n-1). ...

    Text Solution

    |

  10. Equation x^(n)-1=0,ngt1,ninN, has roots 1,a(1),a(2),...,a(n),. The val...

    Text Solution

    |

  11. Equation x^(n)-1=0, ngt1, n in N," has roots "1,a(1),a(2),…,a(n-1). ...

    Text Solution

    |

  12. f(x)=x^(2)+xg'(1)+g''(2)and g(x)=f(1)x^(2)+xf'(x)+f'(x). The value o...

    Text Solution

    |

  13. f(x)=x^(2)+xg'(1)+g''(2)and g(x)=f(1)x^(2)+xf'(x)+f'(x). The value o...

    Text Solution

    |

  14. f(x)=x^(2)+xg'(1)+g''(2)and g(x)=f(1)x^(2)+xf'(x)+f'(x). The domain ...

    Text Solution

    |

  15. g(x+y)=g(x)+g(y)+3xy(x+y)AA x, y in R" and "g'(0)=-4. Number of real...

    Text Solution

    |

  16. g(x+y)=g(x)+g(y)+3xy(x+y)AA x, y in R" and "g'(0)=-4. For which of t...

    Text Solution

    |

  17. g(x+y)=g(x)+g(y)+3xy(x+y)AA x, y in R" and "g'(0)=-4. The value of g...

    Text Solution

    |

  18. A curve is represented parametrically by the equations x=f(t)=a^(In(b^...

    Text Solution

    |

  19. A curve is represented parametrically by the equations x=f(t)=a^(In(b^...

    Text Solution

    |

  20. A curve is represented parametrically by the equations x=f(t)=a^(In(b'...

    Text Solution

    |