Home
Class 12
MATHS
Leg f(x)=x^3+a x^2+b x+5sin^2x be an inc...

Leg `f(x)=x^3+a x^2+b x+5sin^2x` be an increasing function on the set `Rdot` Then find the condition on `aa n dbdot`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BANSAL|Exercise All Questions|425 Videos

Similar Questions

Explore conceptually related problems

Leg f(x)=x^(3)+ax^(2)+bx+5sin^(2)x be an increasing function on the set R. Then find the condition on a and b.

Let f(x)=x^(3)+ax^(2)+bx+5 sin^(2)x be an increasing function on the set R. Then,

Let f(x)=x^(3)+kx^(2)+5x+4sin^(2)x be an increasing function on x in R. Then domain of k is

The function f(x)=x^3-3x^2-24x+5 is an increasing function in the interval

Let f (x) = x ^(3) + ax ^(2) + bx + 5 sin ^2 theta + c be can increasing function of x (theta is a parameter), Then, a and b satisfy the condition:

If g(x)=2x^(3)+lambda x^(2)+mu x+2sin^(2)(x) is increasing AA x in R, then

The function f(x)= [x(x-2)]^2 is increasing in the set

Let f (x) = ax+cos 2x +sin x+ cos x is defined for AA x in R and a in R and is strictely increasing function. If the range of a is [(m)/(n),oo), then find the minimum vlaue of (m- n).

BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. Find the intervals in which the given function increases or decreas...

    Text Solution

    |

  2. Prove the following inequalities 1+cotx\ lt=cotx/2\ AA\ x in (0,pi)

    Text Solution

    |

  3. Leg f(x)=x^3+a x^2+b x+5sin^2x be an increasing function on the set Rd...

    Text Solution

    |

  4. Find the values of x where f(x)=sin(lnx)-cos(lnx) in strictly increasi...

    Text Solution

    |

  5. Prove that sin^2theta<thetasin(sintheta)for0<theta<pi/2dot

    Text Solution

    |

  6. Let f: R->R be a function such that f(x)=a x+3sinx+4cosxdot Then f(x...

    Text Solution

    |

  7. f(x)=(x-2)|x-3| is monotonically increasing in (a)(-oo,5/2)uu(3,oo)...

    Text Solution

    |

  8. A function g(x) is defined as g(x)=1/4f(2x^2-1)+1/2f(1-x^2)a n df(x) ...

    Text Solution

    |

  9. Let f(x)=1-x-x^3.Find all real values of x satisfying the inequality,...

    Text Solution

    |

  10. The intervals of increase of f(x) defined by f(x)=int(-1)^x(t^2+...

    Text Solution

    |

  11. If mean value theorem holds good for the function f(x)=(x-1)/x on ...

    Text Solution

    |

  12. Let f(x)a n dg(x) be two continuous functions defined from RvecR , suc...

    Text Solution

    |

  13. Find the critical points of the function f(x)=2/3sqrt(x^3)-x/2+int1^x(...

    Text Solution

    |

  14. Let f(x)=x+\ sqrt(x)\ "o n"\ [1,4]dot The mean value theorem say...

    Text Solution

    |

  15. Consider f(x)=|1-x|\ \ 1\ lt=xlt=2\ a n d\ \ g(x)=f(x)+bsinpi/2\ ...

    Text Solution

    |

  16. If f is a continuous function on [0,1], differentiable in (0, 1) such ...

    Text Solution

    |

  17. If the function f(x)=2x^2 + 3x + 5 satisfies LMVT at x = 2 on the clo...

    Text Solution

    |

  18. Consider the function f(x)=8x^2-7x+5 on the interval [-6,6]dot Find th...

    Text Solution

    |

  19. Range of the function f(x)=(ln x)/(sqrt(x)) is (a)(-oo,\ e) (b) (-o...

    Text Solution

    |

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

    Text Solution

    |