Home
Class 12
MATHS
Let f : RtoR be a function such that f(x...

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

A

30

B

`-2`

C

`-23`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
`F'' (2) = 6`
` f' = (x) = 3x^2 + 2 x f' (0) + f'(1)`
` f'(0) = f''(1)`
` f'' (x) = 6x + 2f' (0) rArr f'' (1) = 6+2 f'(0)`
`f'(0) = -6, f'' = -6`
`f(x) = x^3 - 6x^2 - 6x + 6`
` f(1) = -5`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST - 18

    VMC MODULES ENGLISH|Exercise MATHEMATICS - SECTION 2|5 Videos

  • JEE MAIN REVISION TEST - 22 JEE - 2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 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. f(x) 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) is

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

Let f:RtoR be a function given by f(x+y)=f(x)f(y) for all x,y in R .If f'(0)=2 then f(x) is equal to

Let f:R->R be a function defined by f(x)=x^2-(x^2)/(1+x^2) . Then:

Let f be a function satisfying f''(x)=x^(-(3)/(2)) , f'(4)=2 and f(0)=0 . Then f(784) equals……..

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f(3) is equal to

Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){-5}

Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){26}

VMC MODULES ENGLISH-JEE MAIN REVISION TEST - 19-MATHEMATICS
  1. Let I=undersetaoversetbint(x^4-2x^2)dx. If is minimum, then the ordere...

    Text Solution

    |

  2. If a circle C passing through the point (4, 0) touches the circle x^(2...

    Text Solution

    |

  3. Let veca = 2hati+lambda1 hatj+3hatk, vec(b)=4hati+(3-lambda2) hatj+6ha...

    Text Solution

    |

  4. If the area enclosed between the curves y=kx^2 and x=ky^2, where kgt0,...

    Text Solution

    |

  5. An unbiased coin is tossed. If the outcome is a head then a pair of un...

    Text Solution

    |

  6. Consider a triangular plot ABC with sides AB = 7 m, BC = 5m and CA = 6...

    Text Solution

    |

  7. The mean of five observations is 5 and their variance is 9.20. If thre...

    Text Solution

    |

  8. Let f : RtoR be a function such that f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3)...

    Text Solution

    |

  9. If the line 5x + 12y - 60 = 0 intersects the x-axis at the point A an...

    Text Solution

    |

  10. Let A be a point on the line vecr = (1- 5 mu) hati + (3mu - 1) hatj + ...

    Text Solution

    |

  11. The equation of a tangent to the hyperbola 9x^2 - 12y^2 = 144 paralle...

    Text Solution

    |

  12. Consider the statement: "P(n): n^(2)-n+41 is prime". Then which one of...

    Text Solution

    |

  13. The sum of all values of theta in (0,(pi)/(2)) satisfying sin^(2)2thet...

    Text Solution

    |

  14. Let nge2 be a natural number and 0ltthetaltpi//2. Then int((sin^ntheta...

    Text Solution

    |

  15. The condition that the parabolas y^2=4c(x-d) and y^2=4ax have a common...

    Text Solution

    |

  16. If underset(i=1)overset(20)Sigma((.^(20)C(i-1))/(.^(20)C(i)+.^(20)C(i-...

    Text Solution

    |

  17. In a class of 140 students numbered 1 to 140, all even numbered studen...

    Text Solution

    |

  18. The sum of all two digit positive numbers which when divided by 7 yiel...

    Text Solution

    |

  19. If the system fo equations x+y+z = 5 x + 2y + 3z = 9 x + 3y + a...

    Text Solution

    |

  20. Consider the quadratic equation (c - 5)x^(2) - 2cx + (c - 4) = 0, c ne...

    Text Solution

    |