Home
Class 12
MATHS
if f(x) be a twice differentiable funct...

if f(x) be a twice differentiable function such that `f(x) =x^(2) " for " x=1,2,3,` then

A

`f''(x)=2 " "AA x in [1,3]`

B

`f''(x) =2 " ""for some " x in (1,3)`

C

`f''(x) =2 " " AA x in (1,3)`

D

`f'(x) =2x " " AA x in (1,3)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-2 Part II|21 Videos
  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-2 Part III|23 Videos
  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise 1 Part III : Match the Column|4 Videos
  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

Similar Questions

Explore conceptually related problems

If f(x) is a twice differentiable function such that f(0)=f(1)=f(2)=0 . Then

If f(x) is a twice differentiable function and given that f(1)=2,f(2)=5 and f(3)=10 then

If f(x) be a differentiable function such that f(x+y)=f(x)+f(y) and f(1)=2 then f'(2) is equal to

If f:R to R is a twice differentiable function such that f''(x) gt 0" for all "x in R, and f(1/2)=1/2, f(1)=1 then :

Let f be a twice differentiable function such that f''(x)=-f(x)" and "f'(x)=g(x)."If "h'(x)=[f(x)]^(2)+[g(x)]^(2), h(a)=8" and "h(0)=2," then "h(2)=

STATEMENT - 1 : Let f be a twice differentiable function such that f'(x) = g(x) and f''(x) = - f (x) . If h'(x) = [f(x)]^(2) + [g (x)]^(2) , h(1) = 8 and h (0) =2 Rightarrow h(2) =14 and STATEMENT - 2 : h''(x)=0

If f(x) is a twice differentiable function such that f(a)=0,f(b)=2,f(c)=-1,f(d)=2,f(e)=0 where a

Let f(x) be twice differentiable function such that f'(0) =2 , then, lim_(xrarr0) (2f(x)-3f(2x)+f(4x))/(x^2) , is

Let f be a twice differentiable function such that f''(x)=-f(x), and f'(x)=g(x),h(x)=[f(x)]^(2)+[g(x)]^(2) Find h(10) if h(5)=11

RESONANCE-APPLICATION OF DERIVATIVES-Exersise-2 Part I
  1. "Let "f(x) ={ underset( x^(2) +8 " "." "x ge0)(-x^(2)" "." "x lt0)...

    Text Solution

    |

  2. Minunun distance between the curves f(x)=e^x and g(x)=ln x is

    Text Solution

    |

  3. The point(s) on the parabola y^2 = 4x which are closest to the circlex...

    Text Solution

    |

  4. If f(x)= a^({a^(|x|)sgn x }),g(x)=a^([a^(|x|)sgn x] for a gt 1, a!=1...

    Text Solution

    |

  5. If f:[1,10]->[1,10] is a non-decreasing function and g:[1,10]->[1,10] ...

    Text Solution

    |

  6. If f(x)=|ax-b|+c|x| is stricly increasing at atleast one point of non ...

    Text Solution

    |

  7. If g(x) is a curve which is obtained by the reflection of f(x) = (e^x...

    Text Solution

    |

  8. The set of values of p for which the points of extremum of the functio...

    Text Solution

    |

  9. The values of parameter a for which the point of minimum of the functi...

    Text Solution

    |

  10. Consider the following statements : S(1): The function y=(2x^(2)-1)...

    Text Solution

    |

  11. Q. Let f (x)=sin^3x+ lambdasin^2x where (pi)/2 ltxlt (pi)/2. The inte...

    Text Solution

    |

  12. "Let "f(x) ={underset(-2x + log(2) (b^(2)-2), x gt1)(x^(3) -x^(2) +10 ...

    Text Solution

    |

  13. Four points A, B, C, D lie in that order on the parabola y = ax^2 +bx+...

    Text Solution

    |

  14. The base of prism is equilateral triangle. The distance from the centr...

    Text Solution

    |

  15. The maximum area of the rectangle whose sides pass through the vertice...

    Text Solution

    |

  16. Statement 1: ABC is given triangle having respective sides a,b,c. D,E,...

    Text Solution

    |

  17. if f'(x)=(x -4) (x-5) (x-6) (x-7) then.

    Text Solution

    |

  18. Show that the square roots of two successive natural numbers greater ...

    Text Solution

    |

  19. If Rolle's theorems applicable to the function f(x)=ln x/x, (x> 0) ove...

    Text Solution

    |

  20. if f(x) be a twice differentiable function such that f(x) =x^(2) " fo...

    Text Solution

    |