Home
Class 12
MATHS
If f(x)={{:(,1,x lt 0),(,1+sin x,0 le x ...

If `f(x)={{:(,1,x lt 0),(,1+sin x,0 le x lt (pi)/(2)):}` then derivative of f(x) x=0

A

is equal to 1

B

is equal to 0

C

is equal to -1

D

does not exist

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 2|56 Videos

Similar Questions

Explore conceptually related problems

If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

Let f(x)={{:(,1+x,"if "x lt 0),(,1+[x]+sin x,0 le x lt pi//2),(,3,x ge pi//2):} Statement-1: F is a continuous on R-[1] Statement-2: The greatest integer function is discontinuous at every integer point.

Let f (x)= [{:(x ^(2)+a,0 le x lt 1),( 2x+b,1le x le 2):}and g (x)=[{:(3x+b,0 le x lt 1),(x ^(3), 1 le x le 2):} If derivative of f(x) w.r.t. g (x ) at x =1 exists and is equal to lamda, then which of the followig is/are correct?

If f(x)={:{(1+sin x", " 0 le x lt pi//2),(" "1 ", " x lt0):} then show that f'(0) does not exist.

Let f(x)={{:(,x^(3)+x^(2)-10x,-1 le x lt 0),(,cos x,0 le x lt pi/2),(,1+sin x,pi/2 le x le pi):}" Then at "x=pi/2 , f(x) has:

If f (x) = tan ^(-1)sqrt((1 + sin x )/(1 - sin x)), 0 le x le (pi)/(2) then f' ((pi)/(6)) =?

If f(x)={{:(-1, x lt 0),(0, x=0 and g(x)=x(1-x^(2))", then"),(1, x gt 0):}

The function f is defined as : f(x)={{:(1","x gt0),(0"," x =0),(-1","x lt 0):} The range of f is :

If f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then continutity and diffrentiability of f(x)

If f(x)={{:(2+x",", x ge0),(4-x",", x lt 0):}, then f (f(x)) is given by :

OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. If f(x)=[x sin pix], then which of the following, is incorrect,

    Text Solution

    |

  2. The function f(x)=1+|sin x|, is

    Text Solution

    |

  3. If f(x)={{:(,1,x lt 0),(,1+sin x,0 le x lt (pi)/(2)):} then derivative...

    Text Solution

    |

  4. Let [x] denotes the greatest integer less than or equal to x and f(x)=...

    Text Solution

    |

  5. A function f : R to R satisfies the equation f(x+y) = f (x) f(y), AA ...

    Text Solution

    |

  6. Let f(x) be defined on R such that f(1)=2,f(2)=8 and f(u+v)=f(u)+kuv-2...

    Text Solution

    |

  7. Let f(x) be a function satisfying f(x+y)=f(x) + f(y) and f(x) = x...

    Text Solution

    |

  8. If f(x)={{:(,ax^(2)-b,|x|lt 1),(,(1)/(|x|),|x| ge1):} is differentiabl...

    Text Solution

    |

  9. If f(x)=(x-x(0)) phi (x) and phi(x) is continuous at x=x(0). Then f'(...

    Text Solution

    |

  10. Let f (x+y) =f (x) f (y) for all x and y, and f(5)=2, f'(0)=3, then f ...

    Text Solution

    |

  11. If f be a function satisfying f(x+y)=f(x)+f(y),AAx,yinR. If f(1) = k, ...

    Text Solution

    |

  12. Let f (x + y) = f(x) f(y) for all x, y, in R, suppose that f(3) = 3...

    Text Solution

    |

  13. Let f(x+y)=f(x)+f(y) and f(x)=x^2g(x)AA x,y in R where g(x) is continu...

    Text Solution

    |

  14. Let f(x+y)=f(x)f(y) for all x, y epsilon R and f(x)=1+x phi (x) l n 2 ...

    Text Solution

    |

  15. Let f(x+y)=f(x) f(y) and f(x)=1+(sin 2x)g(x) where g(x) is continuous....

    Text Solution

    |

  16. Let f(x+y)=f(x) f(y) and f(x)=1+(sin 2x)g(x) where g(x) is continuous....

    Text Solution

    |

  17. Let g(x) be the inverse of an invertible function f(x) which is differ...

    Text Solution

    |

  18. Let g(x) be the inverse of f(x) and f'(x)=1/(1+x^(3)).Find g'(x) in te...

    Text Solution

    |

  19. Let f(x)={{:(,x^(n)sin\ (1)/(x),x ne 0),(,0,x=0):} Then f(x) is contin...

    Text Solution

    |

  20. If for a continuous function f,f(0)=f(1)=0,f'(1)=2 and y(x)=f(e^(x))e^...

    Text Solution

    |