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_____

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-3 Part II|22 Videos
  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise High Level Problems (HLP)|33 Videos
  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-2 Part IV comprehension|11 Videos
  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 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........

RESONANCE-APPLICATION OF DERIVATIVES-Exersise-3 Part I
  1. Match th statements given in Column-I with the intervals//union of in...

    Text Solution

    |

  2. The number of distinct real roots of x^4 - 4 x^3 + 12 x^2 + x - 1 = 0...

    Text Solution

    |

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

    Text Solution

    |

  4. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |

  5. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is 6 (b)...

    Text Solution

    |

  6. A rectangular sheet of fixed perimeter with sides having their lengths...

    Text Solution

    |

  7. A vertical line passing through the point (h,0) intersects the ell...

    Text Solution

    |

  8. The function f(x)=2|x|+|x+2|=||x|2|-2|x|| has a local minimum or a loc...

    Text Solution

    |

  9. Let f[0, 1] -> R (the set of all real numbers be a function.Suppose t...

    Text Solution

    |

  10. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  11. line L:y=mx+3 meets y–axis at E(0, 3) and the are of the parabola y^(2...

    Text Solution

    |

  12. Let a in R and let f: R to R be given by f(x) =x^(5) -5x+a. then

    Text Solution

    |

  13. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

    Text Solution

    |

  14. A cylindrica container is to be made from certain solid material with ...

    Text Solution

    |

  15. Let f,g:[-1,2]rarr RR be continuous functions which are twice differen...

    Text Solution

    |

  16. Let f: R to (0 ,oo)" and " g :R to R be twice differentiable function...

    Text Solution

    |

  17. Which of the following options is the only INCORRECT combination ?

    Text Solution

    |

  18. Which of the following options is the only CORRECT combination

    Text Solution

    |

  19. Which of the following options is the only CORRECT combination ?

    Text Solution

    |

  20. If f:R->R is a twice differentiable function such that f''(x) > 0 for ...

    Text Solution

    |