Home
Class 12
MATHS
Statement-1: The function f(x)\ =\ ln...

Statement-1: The function `f(x)\ =\ ln\ x` is increasing in (0,10) and g(x) = `1/x` is decreasing in (0,10) Statement-2: If a differentiable function increases in the interval `(a , b)` then its derivative function decreases in the interval `(a , b)` .

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BANSAL|Exercise All Questions|425 Videos

Similar Questions

Explore conceptually related problems

The function f(x) = x^2 is increasing in the interval

The function f(x) = x^x decrease on the interval

Statement 1: Both sin xand cos x are decreasing functions in ((pi)/(2),pi) Statement 2: If a differentiable function decreases in an interval (a,b), then its derivative also decreases in (a,b).

the function f(x)=(log x)/(x) is increasing in the interval

The function f(x)=tan^(-1)x-x decreases in the interval.

The function f(x)=tan^(-1)x-x decreases in the interval

If a function f(x) increases in the interval (a,b). then the function phi(x)=[f(x)]^(n) increases in the same interval and phi(x)!=f(x) if

BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. A function y=\ f(x) is defined on [0,4] as f(x)={2x\ \ \ \ if\ 0...

    Text Solution

    |

  2. The function f(x)=(ln(pi+x))/(ln(e+x)) is increasing in (0,oo) decrea...

    Text Solution

    |

  3. Statement-1: The function f(x)\ =\ ln\ x is increasing in (0,10)...

    Text Solution

    |

  4. Statement-1: Suppose f(x)=2^x+1a n d\ g\ (x)=4^(-x)+2^(-x) . The...

    Text Solution

    |

  5. Consider function f(x)={x{x}+1,\ \ \ \ \ \ \ \ \ \ \ \ 0lt=x<1 2-{...

    Text Solution

    |

  6. If f(x)=x+sinx ,g(x)=e^(-x),u=sqrt(c+1)-sqrt(c), v=sqrt(c) -sqrt(c-1...

    Text Solution

    |

  7. The function f(x)= int0^x sqrt(1-t^4)dt is such that: (A) t is defi...

    Text Solution

    |

  8. On which of the following intervals is the function f given by f(x)=x...

    Text Solution

    |

  9. Let f(x)=1+\ x\ ln\ (x+\ sqrt((x^2)+1))-\ sqrt((1)+x^2)a n d\ h(x)=f...

    Text Solution

    |

  10. Let f(x)=a(x-x1)(x-x2)\ w h e r e\ a ,\ x1a n d\ x2\ are real n...

    Text Solution

    |

  11. Let f be a continuous function on R and satisfies f(x)=e^x + int0^1 e^...

    Text Solution

    |

  12. Consider the function f: R->\ R fined as f\ (x)\ =x\ +\ s in\ x . ...

    Text Solution

    |

  13. For the function f(x)\ =\ 1n\ (1-1n\ x) which of the following do ...

    Text Solution

    |

  14. Find the intervals in which f(x)=sinx-cosx , where 0 lt x lt2pi is in...

    Text Solution

    |

  15. Find the greatest & the least values of the following functions in ...

    Text Solution

    |

  16. Find the greatest and the least values of the following functions i...

    Text Solution

    |

  17. If b > a, find the minimum value of |(x-a)^3+|(x-b)^3|, x in R

    Text Solution

    |

  18. The interval to which a may belong so that the function f(x)=(1-(sqrt(...

    Text Solution

    |

  19. If f(x)=2e^x-ae^(-x)+(2a+1)x-3 monotonically increases for AA x in R,...

    Text Solution

    |

  20. Let fa n dg be differentiable on R and suppose f(0)=g(0)a n df^(prime)...

    Text Solution

    |