Home
Class 12
MATHS
If f (x) is continous and differentiable...

If `f (x)` is continous and differentiable in `[-3,9] and f'(x) in [-2,8] AA x in (-3,9).` Let N be the number of divisors of the greatest possible value of `f (9)-f (-3),` then find the sum of digits of N.

Text Solution

Verified by Experts

The correct Answer is:
3
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (MATHCING TYPE PROBLEMS)|6 Videos

  • AREA UNDER CURVES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise AXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

Similar Questions

Explore conceptually related problems

If f (x) is continous on [0,2], differentiable in (0,2) f (0) =2, f(2)=8 and f '(x) le 3 for all x in (0,2), then find the value of f (1).

Let f(x)=a-(x-3)^(8//9) then greatest value of f(x) is

If f(x) is a differentiable function satisfying f^(')(x)lt2 for all xepsilonR and f(1)=2, then greatest possible integral value of f(3) is

If f(x)=a-(x-3)^(8//9) , then the maximum value of f(x) is

if f(x) is differentiable function such that f(1) = sin 1, f (2)= sin 4 and f(3) = sin 9, then the minimum number of distinct roots of f'(x) = 2x cosx^(2) in (1,3) is "_______"

Let f(x)=[9^x-3^x+1] for all x in (-oo, 1), then the range of f(x) is, ([.] denotes the greatest integer function).

Let f(x)=[9^x-3^x+1] for all x in (-oo, 1), then the range of f(x) is, ([.] denotes the greatest integer function).

If f(x) is a differentiable real valued function satisfying f''(x)-3f'(x) gt 3 AA x ge 0 and f'(0)=-1, then f(x)+x AA x gt 0 is

If f(x)=2x-1, find the value of x that makes f(f(x))=9.

If f (x) +2 f (1-x) =x ^(2) +2 AA x in R and f (x) is a differentiable function, then the value of f'(8) is

VIKAS GUPTA (BLACK BOOK) ENGLISH-APPLICATION OF DERIVATIVES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If f (x)= (px)/(e ^(x)) - (x ^(2))/(2) + x is a decreasing function f...

    Text Solution

    |

  2. L e tf(x)={x e^(a x),xlt=0x+a x^2-x^3,x >0 where a is a positive cons...

    Text Solution

    |

  3. Find sum of all possible values of the real parameter 'b' if the diffe...

    Text Solution

    |

  4. Let 'theta' be the angle in radians between the curves (x ^(2))/(36) +...

    Text Solution

    |

  5. Let set of all possible values of lamda such that f (x)= e ^(2x) - (la...

    Text Solution

    |

  6. Let a,b,c and d be non-negative real number such that a ^(5)+b^(5) le ...

    Text Solution

    |

  7. There is a point (p,q) on the graph of f(x)=x^(2) and a point (r,s) on...

    Text Solution

    |

  8. If f(x)=max| 2 siny-x|, (where y in R), then find the minimum value o...

    Text Solution

    |

  9. Let f (x) = int (0)^(x) ((a -1) (t ^(2)+t+1)^(2) -(a+1)(t^(4)+t ^(2) +...

    Text Solution

    |

  10. The numbr of real roots of the equation x ^(2013)+ e ^(2014x) =0 is

    Text Solution

    |

  11. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |

  12. The least positive integral value of 'k' for which there exists at lea...

    Text Solution

    |

  13. The coordinates of a particle moving in a plane are given by x (t) = a...

    Text Solution

    |

  14. A tank contains 100 litres of fresh water. A solution containing 1 gm/...

    Text Solution

    |

  15. If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...

    Text Solution

    |

  16. It is given that f (x) is defined on R satisfying f (1)=1 and for AA ...

    Text Solution

    |

  17. The number of normals to the curve 3y ^(3) =4x which passes through th...

    Text Solution

    |

  18. Find the number of real root (s) of the equation ae ^(x) =1+ x + (x ^(...

    Text Solution

    |

  19. Let f (x) = ax+cos 2x +sin x+ cos x is defined for AA x in R and a in...

    Text Solution

    |

  20. If p (1) and p(2) are the lengths of the perpendiculars from origin on...

    Text Solution

    |