Home
Class 12
MATHS
Let p(x) be a real polynomial of least d...

Let `p(x)` be a real polynomial of least degree which has a local maximum at `x=1` and a local minimum at `x=3.` If `p(1)=6a n dp(3)=2,` then `p^(prime)(0)` is_____

Text Solution

Verified by Experts

The correct Answer is:
9
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|11 Videos
  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos
  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

Let p(x) be a real polynomial of least degree which has a local maximum at x=1 and a local minimum at x=3. If p(1)=6 and p(3)=2, then p'(0) is

If P (x) be a polynomial of degree three that has a local maximum value 8 at x=1 and a local minimum value 4 at x=2 , then p (0 ) is equal to :

Let f(x) be a cubic polynomial which is having local maximum at (1,2) and f'(x) has local extrema at x=0 .If f(0)=1 then

Let g (x) be a cubic polnomial having local maximum at x=-1 and g '(x) has a local minimum at x =1, If g (-1) =10 g, (3) =- 22, then

Consider a polynomial P(x) of the least degree that has a maximum equal to 6 at x=1 and a minimum equal to 2 at x=3. Then the value of p(2)+P(0)-7 is

If P(x) is a polynomial of the least degree that has a maximum equal to 6 at x=1, and a minimum equalto 2 at x=3, then int_(0)^(1)P(x)dx equals:

Let P(x) be a real polynomial of degree 3 which vanishes at x=-3. Let P(x) have local minima at x=1, local maximum at x=-1 and underset(-1)overset(1)int P(x)dx=-18 , then the sum of all the coefficients of the polynomical P(x) is equal to........

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If f(x)=x^(3)+bx^(2)+cx+dand 0 ltb^(2)ltc, then in (-oo,oo)

    Text Solution

    |

  2. If f(x)=x^(2)+2bx+2c^(2)and g(x)=-x^(2)-2cx+b^(2), such that minf(x)gt...

    Text Solution

    |

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

    Text Solution

    |

  4. If f(x)=e^(1-x) then f(x) is

    Text Solution

    |

  5. The maximum value of (cosalpha(1))-(cos alpha(2))...(cosalpha(n)), u...

    Text Solution

    |

  6. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

    Text Solution

    |

  7. If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=...

    Text Solution

    |

  8. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  9. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  10. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  11. For the circle x^(2)+y^(2)=r^(2), find the value of r for which the ar...

    Text Solution

    |

  12. Find a point on the curve x^2 + 2y^2 = 6, whose distance from the li...

    Text Solution

    |

  13. Let f:R rArr R be defined as f(x)=|x|+|x^2-1| The total number of p...

    Text Solution

    |

  14. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  15. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  16. The maximum value of the expression (1)/(sin^(2)theta+3sinthetacosthet...

    Text Solution

    |

  17. The maximum value of the function f(x)=2x^(3)-15x^(2)+36x-48 on the se...

    Text Solution

    |

  18. A wire of length 2 units is cut into two parts which are bent respecti...

    Text Solution

    |

  19. If x = -1 and x = 2 are extreme points of f(x) = alpha log|x| + beta x...

    Text Solution

    |

  20. Let a, b R be such that the function f given by f(x)""=""ln""|x|""+""...

    Text Solution

    |