Home
Class 12
MATHS
If f:R->R is a twice differentiable func...

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

A

`f'(1) le 0`

B

`f'(1) gt1`

C

`0 lt f'(1) le (1)/(2)`

D

`(1)/(2) lt f'(1) le 1`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Exersise-3 Part II|22 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise High Level Problems (HLP)|35 Videos

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Exersise-2 Part IV comprehension|7 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

Similar Questions

Explore conceptually related problems

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

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

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then f(x) is

Let f be the continuous and differentiable function such that f(x)=f(2-x), forall x in R and g(x)=f(1+x), then

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to

Let f: \mathbb{R} rarr \mathbb{R} be a twice differentiable function such that f(x+pi)=f(x) and f''(x) + f(x) geq 0 for all x in \mathbb{R} . Show that f(x) geq 0 for all x in \mathbb{R} .

Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA , x,y in R, y!=0 and f(1)!=0 , f'(1)=3 then

Let f be a differentiable function from R to R such that |f(x) - f(y) | le 2|x-y|^(3/2), for all x, y in R . If f(0) =1, then int_(0)^(1) f^(2)(x) dx is equal to

Let f:R to R and g:R to R be differentiable functions such that f(x)=x^(3)+3x+2, g(f(x))=x"for all "x in R , Then, g'(2)=

RESONANCE ENGLISH-APPLICATION OF DERIVATIVES-Exersise-3 Part I
  1. If f(x) is a polynomial of degree 4 having extremum at x=1,2 and lim(x...

    Text Solution

    |

  2. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  3. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  4. The number of distinct real roots of x^4-4x^3+12 x 62+x-1=0i sdot

    Text Solution

    |

  5. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  6. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |

  7. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

    Text Solution

    |

  8. A rectangular sheet of fixed perimeter with sides having their lengths...

    Text Solution

    |

  9. A vertical line passing through the point (h, 0) intersects the ellips...

    Text Solution

    |

  10. The funciton f(X) =2|x|+|x+2|-||x+2|-|x|| has a local mimimum or a lo...

    Text Solution

    |

  11. Let f:[0,1]rarrR be a function. Suppose the function f is twice differ...

    Text Solution

    |

  12. Let a in R and let f: Rvec be given by f(x)=x^5-5x+a , then (a) f(x...

    Text Solution

    |

  13. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

    Text Solution

    |

  14. A cylindrical container is to be made from certain solid material with...

    Text Solution

    |

  15. Let f,g:[-1,2]vecR be continuous functions which are twice differentia...

    Text Solution

    |

  16. Let f:Rrarr(0,oo)andg:RrarrR be twice differentiable functions such th...

    Text Solution

    |

  17. If f:R->R is a twice differentiable function such that f''(x) > 0 for ...

    Text Solution

    |

  18. If f:R is a differentiable fucntion such that f(x) gt 2f(x) for all x...

    Text Solution

    |

  19. If f(x) = \begin{vmatrix} cos2x & cos2x & sin2x \\ -cosx & cosx & -...

    Text Solution

    |

  20. For every twice differentiable function f: R to [-2,2] with (f^(0))^(2...

    Text Solution

    |