Home
Class 11
MATHS
Given P(x)=x^(4)+ax^(3)+bx^(2)+cx +d suc...

Given `P(x)=x^(4)+ax^(3)+bx^(2)+cx +d` such that x=0 is the only real root of `P'(x)==0`. If `P(-1) lt P(1)`, then in the interval [-1,1]

Text Solution

Verified by Experts

The correct Answer is:
`P(1) therefore P_("min") = P(0)`
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise Exercise - 8.1 (Long Answer Questions)|24 Videos
  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise Exercise - 8.2 (Long Answer Questions)|36 Videos
  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise Examples|3 Videos
  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos
  • MEAN VALUE THEOREMS

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I (LEVEL-II (MORE THAN ONE CORRECT ANSWER TYPE QUESTIONS ) )|2 Videos

Similar Questions

Explore conceptually related problems

If one root of x^(2) - (p - 1) x + 10 = 0 is 5 then p =

If the roots of ax^(3) + bx^(2) + cx +d = 0 are in H.P then the roots of dx^(3) - cx^(2) + bx - a = 0 are in

If the roots of ax^(3) + bx^(2) + cx +d = 0 are in A.P then the roots of dx^(3) + cx^(2) + bx + a = 0 are in

If the roots of ax^(3) + bx^(2) + cx +d = 0 are in G.P then the roots of dx^(3) - cx^(2) + bx - a = 0 are in

If the equation (cos p - 1)x^(2) + cos p x + sin p =0 in the varable x has real roots then p can taken any value in the interval

If the roots of ax^(3) + bx^(2) +cx + d = 0 are in G.P. then the roots of ak^(3) x^(3) + bk^(2) x^(2) + ckx + d = 0 are in

If X is a Poisson variable with P(X=0)=P(X=1) then P(X=2)=

AAKASH SERIES-MAXIMA AND MINIMA -Advanced Analytical Solved Examples
  1. Find the least value of k for which the function x^(3) + kx +1 is an i...

    Text Solution

    |

  2. Find the values of a if f(x) = 2x^(x) - a e^(-x) + (2a +1) x-3 is incr...

    Text Solution

    |

  3. Separate the intervals of monotonicity of the following functions : ...

    Text Solution

    |

  4. Separate the intervals of monotonicity of the following functions : ...

    Text Solution

    |

  5. Let f(x) and g(x) be two continous functions defined from Rrarr R, suc...

    Text Solution

    |

  6. Prove that |cos alpha - cos beta| le | alpha - beta|.

    Text Solution

    |

  7. For 0 lt x lt (pi)/(2), prove that cos (sin x) gt sin (cos x).

    Text Solution

    |

  8. Examine for maxima or minima for f(x) = {(x^(2),",",x lt 0,),(5,",","x...

    Text Solution

    |

  9. f(x) = {(cos""(pix)/(2),",",x gt 0,),("x + a",",",x le 0,):}. Find the...

    Text Solution

    |

  10. Discuss the extremum of f(x) = 2x + 3x^(2//3).

    Text Solution

    |

  11. Discuss the global maxima and global minima for f(x) = tan^(-1) x - lo...

    Text Solution

    |

  12. Let f(x) = {(x^(3) - x^(2) + 10x - 5",", x le 1),(-2x + log(2)(b^(2) -...

    Text Solution

    |

  13. The maximum value of ( cos alpha1) ( cos alpha2) … ( cos alphan) under...

    Text Solution

    |

  14. Let a, b, c be positive number. If ax^(2) + (b)/(x) = c for all x gt 0...

    Text Solution

    |

  15. If f(x) = 2sin^(3) x + lambda sin^(2) x, x - (pi)/(2) lt x lt (pi)/(2)...

    Text Solution

    |

  16. Let f''(x) gt 0 AA x in R and g(x) = g(x) = 2f((x^(2))/(2)) + f(6-x^(2...

    Text Solution

    |

  17. If the equation x^(4) + 4x^(3) - 2x^(2) - 12 x + k = 0 has 4 real root...

    Text Solution

    |

  18. One corner of a rectangle of width one unit is folded over so as to re...

    Text Solution

    |

  19. Given P(x)=x^(4)+ax^(3)+bx^(2)+cx +d such that x=0 is the only real ro...

    Text Solution

    |

  20. Show that the function f(x) = 2x^(2) - 3(lambda + 2) x^(2) + 2 lambdax...

    Text Solution

    |