Home
Class 12
MATHS
If f(x)=ax^3+bx^2+cx+d has local extrem...

If `f(x)=ax^3+bx^2+cx+d` has local extrema at two points of opposite signs than prove that roods of the quadratic `ax^2+bx+c=0` are real and distinct.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

IF a,b,c are in G.P prove that the roots of the equation ax^2+2bx+c=0 are equal.

If the two roots of the equation ax^2 + bx + c = 0 are distinct and real then

IF the signs of a and c are opposite to that of b then both roots of the equation ax^2+bx+c=0 are-

If the roots alpha and beta of the quadratic equation ax^2+bx+c =0 are real and of opposite sign.then show that roots of the equation alpha(x-beta)^2+beta(x-alpha)^2 =0 are also real and of opposite sign.

If alpha,beta are the roots of the quadratic equation ax^2+bx+c=0 and 3b^2=16ac then

If one of the root of the quadratic equation ax^2+bx+c=0,(a!=0) be zero then

If alpha, beta are the roots of the quadratic equation ax^(2)+bx+c=0 and 3b^(2)=16 ac then

The perfect square form of the quadratic equation ax^(2)+bx+c=0(ane0) is

Find the condition for which the roots of the quadratic equation ax^2+bx+c=0(ane0) are both positive

If alpha,beta are the roots of the quadratic equation ax^(2)+bx+c=0and3b^(2)=16ac then-

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. Find lim(x->0)(sin(pisin^2(x))/x^2)

    Text Solution

    |

  2. lim(x to 0) (1-cosx)/x^2 = ?

    Text Solution

    |

  3. If f(x)=ax^3+bx^2+cx+d has local extrema at two points of opposite si...

    Text Solution

    |

  4. Prove that if 2a0^2lt15a all roots of x^5-a0x^4+3ax^3+bx^2+cx+d=0 can...

    Text Solution

    |

  5. Let a,b,c be real. If ax^2+bx+c=0 has two real roots alpha,beta where ...

    Text Solution

    |

  6. Let a+b=4, where a gt 2 and let g(x)be a differentiable function. If ...

    Text Solution

    |

  7. On the curve x^3=12y the abscissa changes at a faster rate than the or...

    Text Solution

    |

  8. A spherical iron ball 10 cm in radius is coated with a layer of ice of...

    Text Solution

    |

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

    Text Solution

    |

  10. The function f(x)=2log(x-2)-x^2+4x+1 increases in the interval

    Text Solution

    |

  11. The function f(x)=sin^4x+cos^4x increasing if :

    Text Solution

    |

  12. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  13. The function f(x) =tan^(-1)(sinx+cosx) is an increasing function in

    Text Solution

    |

  14. The function f defined by f(x)=4x^4-2x+1 is increasing for

    Text Solution

    |

  15. The value of a for which the functionf(x)=asinx+1/3sin3x has an extrem...

    Text Solution

    |

  16. xgt0,ygt0 and x+y=1. The minimum value of xlogx+ylogy is

    Text Solution

    |

  17. The minimum value of 2log10x-logx0.01. xgt1, is

    Text Solution

    |

  18. The maximum slope of the curve y=-x^3+3x^2+2x-27 is

    Text Solution

    |

  19. For the function f(x)=xe^x, the point

    Text Solution

    |

  20. The minimum value of logax+logxa,0ltxlta, is

    Text Solution

    |