Home
Class 12
MATHS
If P(x) = a 0 + a 1 x ^(2) + a 2 x^(4)...

If `P(x) = a _0 + a _1 x ^(2) + a _2 x^(4) + … + a _n x ^(2n)` is a polynomial in a real variable `x` with `0 lt a _0 lt a _1 lt a _2 lt … lt a_n`. Then, the function `P (x)` has

A

exactly one maximum

B

exactly one minimum

C

one maximum and one minimum

D

none of these

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Maxima and Minima

    A DAS GUPTA|Exercise EXERCISE|59 Videos
  • Main Tests

    A DAS GUPTA|Exercise Exercise|8 Videos
  • Miscellaneous Exercises

    A DAS GUPTA|Exercise Exercise|77 Videos

Similar Questions

Explore conceptually related problems

If cosx = (1)/(2) and 0 lt x lt 2pi then solutions are

If f(x)= kx, 0 lt x lt 2 = 0 otherwise, is a probability density function of a random variable X , then find (i) value of k, (ii) P(1 lt x lt2).

If 0 lt x lt (pi)/(2) , then ("sin x + cosec x") is

0 lt a lt 2 pi , sin^(-1)(sin a ) lt x^(2)-2x for all x in I then a in

Let f(x)=(sinpix)/(x^(2)), x gt 0 The x_(1) lt x_(2) lt x_(3) . . . lt x_(n)lt .. . be all points of local maximum of f(x) and y^(1) lt y_(2) lt y_(3) . . . lt y_(n) lt . . . be all the points of lcal minimum of f(x) then correct options is/are

A DAS GUPTA-Maxima and Minima-EXERCISE
  1. What is the area of the largest triangle that can be inscribed in a se...

    Text Solution

    |

  2. x and y be two variables such that xgt0 and xy=1. Then the minimum val...

    Text Solution

    |

  3. The value of a so that the sum of the squares of the roots of the equa...

    Text Solution

    |

  4. Twenty metres of wire is available for fencing off a flower-bed in ...

    Text Solution

    |

  5. The total cost of making n pocket radios per day is Rs{(n^2)/4 +35n + ...

    Text Solution

    |

  6. A telephone company in a town has 500 subscribers on its list and c...

    Text Solution

    |

  7. If P(x) = a 0 + a 1 x ^(2) + a 2 x^(4) + … + a n x ^(2n) is a polyn...

    Text Solution

    |

  8. Find the minimum length of radius vector of the curve (a^2)/(x^2)+(b^...

    Text Solution

    |

  9. A right cylindrical vessel of a given capacity is formed using least p...

    Text Solution

    |

  10. Let f(x) =(x-1)^p.(x-2)^q where p > 1, q > 1. Each critical point of f...

    Text Solution

    |

  11. The point (0, 3) is closest to the curve x^2 = 2y at

    Text Solution

    |

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

    Text Solution

    |

  13. Let f(x) be a function such that f'(a) ne 0 . Then , at x=a, f(x)

    Text Solution

    |

  14. N Characters of information are held on magnetic tape, in batches of x...

    Text Solution

    |

  15. The function f(x) = x^2+a/xcannot have a maximum at x = -3 for any rea...

    Text Solution

    |

  16. Find the maximum slope of the curve y=-x^3+3x^2+2x-27 .

    Text Solution

    |

  17. Two points A(1, 4) & B(3, 0) are given on the ellipse 2x^(2) + y^(2) =...

    Text Solution

    |

  18. If f(x)=alog|x|+b x^2+x has its extremum values at x=-1a n dx=2, then ...

    Text Solution

    |

  19. P is a variable point on the curve y= f(x) and A is a fixed point in...

    Text Solution

    |

  20. The fuel charges for running a train are proportional to the square of...

    Text Solution

    |