Home
Class 11
MATHS
If f(x)=x^3+ax^2+bx+5sin^2x increase for...

If `f(x)=x^3+ax^2+bx+5sin^2x` increase for all `x in R` show that `a^2-3b+15lt0`

Promotional Banner

Topper's Solved these Questions

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise SYNOPSIS|22 Videos

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-I|31 Videos

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-7.2 LONG ANSWER QUESTIONS)|3 Videos

  • MATRICES

    AAKASH SERIES|Exercise LINEAR EQUATIONS - PRACTICE EXERCISE|15 Videos

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL - II (PRACTICE SHEET )(ADVANCED)) (INTEGER TYPE QUESTIONS)|3 Videos

Similar Questions

Explore conceptually related problems

If f(x) =x^(3) +ax^(2)+bx +5 sin^(2) x is an increasing function on R, then

Show that f(x) = x^(3) + 3ax^(2) + 3a^(2) + b is increasing on R for all values of a and b.

The function f(x) =x^3+ax^2+bx+c,a^2lt=3b has

Find f'(x)" if "f(x)= (sin x)^(sin x) for all 0 lt x lt pi .

If f(x) = x^(3) + bx^(2) +ax satisfies the conditions of Rolle's theorem on [1,3] with c = 2+(1)/(sqrt(3)) then (a,b) =0

The condition that =x^(3)+ax^(2)+bx+c is an increasing function for all real values of 'x' is

AAKASH SERIES-MAXIMA & MINIMA-ADDITIONAL EXERCISE
  1. Find the intervals in which the following functions are strictly incre...

    Text Solution

    |

  2. Find the intervals in which the following functions are strictly incre...

    Text Solution

    |

  3. If f(x)=x^3+ax^2+bx+5sin^2x increase for all x in R show that a^2-3b+1...

    Text Solution

    |

  4. Show that x^(1//x) is increasing in (0,e) and decreasing in (e,oo). He...

    Text Solution

    |

  5. Find the maximum and minimum values, if any, of the functions given by...

    Text Solution

    |

  6. Find the maximum and minimum values, if any, of the functions given by...

    Text Solution

    |

  7. Find the maximum and minimum values, if any, of the functions given by...

    Text Solution

    |

  8. Find the points of local maximum or local minimum for the following ...

    Text Solution

    |

  9. Find the points of local maximum or local minimum for the following ...

    Text Solution

    |

  10. The minimum value of a^2sec^2theta +b^2 cosec^2 theta is

    Text Solution

    |

  11. If y = a log|x| + bx^(2) + x has extreme values at x = 2 and x = -4/3 ...

    Text Solution

    |

  12. If y=(ax+b)/((x-1)(x-4)) has a maximum value at the point (2,-1) then

    Text Solution

    |

  13. A cubic function of x ahs maximum 10 and minimum -5//2, when x=-3 and ...

    Text Solution

    |

  14. Find the triangle of the greatest area among the right triangles of a ...

    Text Solution

    |

  15. Find the greatest rectangle that can be inscribed in x^2/a^2+y^2/b^2=1

    Text Solution

    |

  16. If the perimeter of a sector of a circle is constant then find the ang...

    Text Solution

    |

  17. Show that a conical tent of given capacity will require the least amou...

    Text Solution

    |

  18. The volume of the greatest cylinder which can be inscribed in a cone o...

    Text Solution

    |

  19. A wire of length 'a' is cut into two parts which are bent in the form ...

    Text Solution

    |

  20. An open box of maximum volume is made from a square piece of tin of si...

    Text Solution

    |