Home
Class 12
MATHS
Write the set of values of a for which f...

Write the set of values of `a` for which `f(x)=cosx+a^2\ x+b` is strictly increasing on `R` .

Text Solution

Verified by Experts

`f(x)=cos x+a^{2} x+b`
` f^{prime}(x)=-sin x+a^{2}`
for strictly increasing
` f^{prime}(x)>0`
` ...
Promotional Banner

Topper's Solved these Questions

  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos
  • INDEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|1401 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=((a^(2)-4)/(a^(2)+2))x^(3)-3x+sin3, then the true set of values of a for which f(x) is strictly decreasing on R is

Prove that f(x) = 3^(x) is strictly increasing on R

Find the set of values of 'a' for which f(x)=x+cos x+ax+b is increasing on R

Write the set of values of 'a' for which f(x)=(log)_(a)x is increasing in its domain.

Write the set of values of k for which f(x)=kx-sin x is increasing on R .

Find the complete set of values of lambda, for which the function f(x)={x+1,x 1 is strictly increasing at x=1

Write the set of values of a for which the function f(x)=ax+b is decreasing for all x in R.

Find the values of 'x' for which f(x)=x^(x),x gt 0 is strictly increasing or decreasing.

Show that the function f(x) = 2x+1 is strictly increasing on R.

Prove that f (x) = e^(3x) is strictly increasing function on R.

RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. Write the interval in which f(x)=sinx+cosx ,\ \ x in [0,\ pi//2] is in...

    Text Solution

    |

  2. State whether f(x)=tanx-x is increasing or decreasing its domain.

    Text Solution

    |

  3. Write the set of values of a for which f(x)=cosx+a^2\ x+b is strictly ...

    Text Solution

    |

  4. The interval of increase of the function f(x)=x-e^x+tan(2pi//7) is (a)...

    Text Solution

    |

  5. The function f(x)=cot^(-1)x+x increases in the interval (a) (1,\ oo) ...

    Text Solution

    |

  6. The function f(x)=x^x decreases on the interval (a) (0,\ e) (b) (0,\ ...

    Text Solution

    |

  7. The function f(x)=2log(x-2)-x^2+4x+1 increases on the interval (a) (1,...

    Text Solution

    |

  8. If the function f(x)=2x^2-k x+5 is increasing on [1,\ 2] , then k lies...

    Text Solution

    |

  9. IF f(x)=x^3+a x^2+b x+5sin^2x\ is a strictly increasing functio...

    Text Solution

    |

  10. The function f(x)=(log)e(x^3+sqrt(x^6+1)) is of the following types: (...

    Text Solution

    |

  11. If the function f(x)=2tanx+(2a+1)(log)e|secx|+(a-2)x is increasing on ...

    Text Solution

    |

  12. Let f(x)=tan^(-1)(g(x)) , where g(x) is monotonically increasing for 0...

    Text Solution

    |

  13. Let f(x)=x^3-6x^2+15 x+3 . Then, (a) f(x)>0 for all x in R (b) f(x)>...

    Text Solution

    |

  14. The function f(x)=x^2\ e^(-x) is monotonic increasing when (a) x in R...

    Text Solution

    |

  15. Function f(x)=cosx-2\ lambda\ x is monotonic decreasing when (a) lambd...

    Text Solution

    |

  16. In the interval (1,\ 2) , function f(x)=2|x-1|+3|x-2| is (a) monotonic...

    Text Solution

    |

  17. Function f(x)=x^3-27 x+5 is monotonically increasing when (a) x<-3 (b...

    Text Solution

    |

  18. Function f(x)=2x^3-9x^2+12 x+29 is monotonically decreasing when (a) x...

    Text Solution

    |

  19. If f(x)=k x^3-9x^2+9x+3 monotonically increasing in R , then k<3 (b) ...

    Text Solution

    |

  20. f(x)=2x-tan^(-1)x-log{x+sqrt(x^2+1)} is monotonically increasing when ...

    Text Solution

    |