Home
Class 12
MATHS
If f(x)={{:(x^(2)"sin"(1)/(x)",",x ne0),...

If `f(x)={{:(x^(2)"sin"(1)/(x)",",x ne0),(k",",x=0):}`

A

f has a continous derivative `AA x in R`

B

f is a bounded function

C

f has an global minimum at `x=0`

D

f" is continous `AA x in R`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|15 Videos
  • APPLICATION OF DERIVATIVES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (MATHCING TYPE PROBLEMS)|6 Videos
  • APPLICATION OF DERIVATIVES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|22 Videos
  • AREA UNDER CURVES

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

Similar Questions

Explore conceptually related problems

Let f(x)={{:(x sin.(1)/(x)",",x ne0),(0",",x=0):}} and g(x)={{:(x^(2)sin.(1)/(x)",", x ne 0),(0",", x=0):}} Discuss the graph for f(x) and g(x), and evaluate the continuity and differentiabilityof f(x) and g(x).

Let g(x)=xf(x) , where f(x)={{:(x^(2)sin.(1)/(x),":",x ne0),(0,":",x=0):} . At x=0 ,

If f(x)={{:(,x^(2)sin((1)/(x)),x ne 0),(,0, x=0):} , then

If f(x)={{:(,x^(m)sin((1)/(x)),x ne 0),(,0,x=0):} is a continous at x=0, then

Show that the function defined by f(x) = {{:(x^(2) sin 1//x",",x ne 0),(0",",x = 0):} is differentiable for every value of x, but the derivative is not continuous for x=0

If f(x)={{:(x^(p+1)cos.(1)/(x)":", x ne 0),(0":", x=0):} then at x = 0 the function f(x) is

If f(x)={{:((sinpix)/(5x)",",x ne0),(k,","0):} is continuous at x=0 , then k is equal to

Let f(x)={{:(,x^(n)sin\ (1)/(x),x ne 0),(,0,x=0):} Then f(x) is continuous but not differentiable at x=0 . If

Discuss the continuity of f(x) ={:{(sin""(1)/(x)", "x ne 0),(" "1", " x= 0):},

A function f :R to R is given by f (x) = {{:(x ^(4) (2+ sin ""(1)/(x)), x ne0),(0, x=0):}, then

VIKAS GUPTA (BLACK BOOK) ENGLISH-APPLICATION OF DERIVATIVES -EXERCISE (ONE OR MORE THAN ANSWER IS/ARE CORRECT )
  1. Let f: [0, 8]to R be differentiable function such that f (0) =0, f (4)...

    Text Solution

    |

  2. If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

    Text Solution

    |

  3. If f(x)={{:(x^(2)"sin"(1)/(x)",",x ne0),(k",",x=0):}

    Text Solution

    |

  4. If f ''(x)|le 1 AA x in R, and f (0) =0=f' (0), then which of the fol...

    Text Solution

    |

  5. Let f : [-3, 4] to R such that f ''(x) gt 0 for all x in [-3,4], then ...

    Text Solution

    |

  6. Let f (x) be twice differentialbe function such that f'' (x) gt 0 in [...

    Text Solution

    |

  7. Let g (x) be a cubic polnomial having local maximum at x=-1 and g '(x)...

    Text Solution

    |

  8. Let S be the set of real values of parameter lamda for which the equat...

    Text Solution

    |

  9. The function f (x) =1+ x ln (x+ sqrt(1+ x ^(2)))-sqrt(1- x^(2)) is:

    Text Solution

    |

  10. Let m and n be positive integers and x,y gt 0 and x+y =k, where k is c...

    Text Solution

    |

  11. Determine the equation of straight line which is tangent at one point ...

    Text Solution

    |

  12. A curve is such that the ratio of the subnomal at any point to the sum...

    Text Solution

    |

  13. Number of A parabola of the form y= ax^2 +bx+c with a>0 intersectio...

    Text Solution

    |

  14. Find the gradient of the line passing through the point (2,8) and touc...

    Text Solution

    |

  15. The equation x + cos x = a has exactly one positive root. Complete set...

    Text Solution

    |

  16. Given that f (x) is a non-constant linear function. Then the curves :

    Text Solution

    |

  17. f (x) = int (0) ^(x) e ^(t ^(3)) (t ^(2) -1) (t+1) ^(2011) dt (x gt ...

    Text Solution

    |

  18. Let f(x)=sinx+a x+bdot Then which of the following is/are true? (a) f(...

    Text Solution

    |

  19. Which of the following graphs represent function whose derivatives hav...

    Text Solution

    |

  20. Consider f (x)= sin ^(5) x-1, x in [0, (pi)/(2)], which of the followi...

    Text Solution

    |