Home
Class 12
MATHS
Find the values of ' a ' for which the f...

Find the values of `' a '` for which the function `f(x)=sinx-a x+4` is increasing function on `R` .

Text Solution

Verified by Experts

The value of a for which the function f(x) = sinx -ax +b increases on R are `(-infty,-1)`.
`therefore f^(')(x)= cosx-a`
and `f^(')(x) gt 0 rArr cos gta`
Since, `cosx in [-1,1]`
`rArr a larr1 rArr in (-infty, -1)`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR|Exercise Application Of Integrals|68 Videos

Similar Questions

Explore conceptually related problems

Find the values of ' a ' for which the function f(x)=sin x-ax+4 is increasing function on R.

Find the values of b for which the function f(x)=sin x-bx+c is a decreasing function on R .

Find the values of b for which the function f(x)=sin x-bx+c is a decreasing function on R.

The function f(x)=x+sinx has

Find the values of 'a' for which the function : f(x)=x^(2)-2ax+6 is increasing when x gt 0 .

Find the values of x, for which the function f(x)=x^(3)+12x^(2)+36x+6 is increasing.

Is the function f(x)=x^(2), x in R increasing?

Show that the function f(x) = x -sin x is an increasing function forall x in R .

Find the value of a for which the function f(x) =x^(2)-2ax+6,x gt 0 is strictly increasing.

NCERT EXEMPLAR-APPLICATION OF DERIVATIVES-Application Of Derivatives
  1. The two curves x^3-3xy^2+2=0 and 3x^2y-y^3-2=0

    Text Solution

    |

  2. 24. Find the intervals in which the following function is (a) increasi...

    Text Solution

    |

  3. The function f:R rarr R be defined by f(x)=2x+cosx then f

    Text Solution

    |

  4. If y=x(x-3)^(2) decreases for the values of x given by

    Text Solution

    |

  5. The function f(x) =4sin^(3)x-6sin^(2)x +12 sinx + 100 is strictly

    Text Solution

    |

  6. Which of the following functions are decreasing on (0,\ pi//2) ? (i) c...

    Text Solution

    |

  7. The function f(x)= tan x - x

    Text Solution

    |

  8. If x is real, then the minimum value of the expression x^2-8x+17 is

    Text Solution

    |

  9. Show that the least value of the function f(x)=x^3-18 x^2+96 x in the ...

    Text Solution

    |

  10. Show that the least value of the function f(x)=2x^3-3x^2-12x+1 on [-2,...

    Text Solution

    |

  11. Show that The maximum value of sinx. cosx in R is 1/2

    Text Solution

    |

  12. At x=(5pi)/6,\ \ f(x)=2sin3x+3cos3x is

    Text Solution

    |

  13. The maximum slope of curve y =-x^(3)+3x^(2)+9x-27 is

    Text Solution

    |

  14. The function f(x)=x^(x) has a stationary point at

    Text Solution

    |

  15. Show that the maximum value of (1/x)^x is e^(1//e) .

    Text Solution

    |

  16. The curves y=4x^(2)+2x-8 and y=x^(3)-x+13 touch each other at the poin...

    Text Solution

    |

  17. The equation of normal to the curve y=tanx at (0,0) is ………………..

    Text Solution

    |

  18. Find the values of ' a ' for which the function f(x)=sinx-a x+4 is inc...

    Text Solution

    |

  19. The function f(x)=(2x^2-1)/x^4, x gt 0decreases in the interval

    Text Solution

    |

  20. The least function value of function f(x) =ax + b/x (where, a gt 0, b ...

    Text Solution

    |