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.`
f(x) is

A

one-one and onto

B

one-one and into

C

many-one and onto

D

many-one and into

Text Solution

AI Generated Solution

To solve the problem, we need to find the function \( f(x) \) given the equation: \[ f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3) \] ### Step 1: Define variables for derivatives Let's denote: ...
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) is

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

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

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 f : R rarr R be defined by f(x) = x^(2) - 3x + 4 for all x in R , then f (2) is equal to

Let f(x)=x^3-6x^2+15 x+3 . Then, (a) f(x)>0 for all x in R (b) f(x)>f(x+1) for all x in R (c) f(x) is invertible (d) f(x)<0 for all x in R

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:R to R be given by f(x+y)=f(x)-f(y)+2xy+1"for all "x,y in R If f(x) is everywhere differentiable and f'(0)=1 , then f'(x)=

If f(x)=x^3+x^2f(1)+xf\'\'(2)+f\'\'\'(3). Then f(2) is (a) -2 (b) 1 (c) 30 (d) 2

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

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    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 domain ...

    Text Solution

    |

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

    Text Solution

    |

  15. 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

    |

  16. 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

    |

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

    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. Let f: R rarr R be a differentiable function satisfying f(x+y)=f(x)+f(...

    Text Solution

    |