Home
Class 12
MATHS
Let P(x)=a0+a1x^2+a2x^4+...+an x^(2n) be...

Let `P(x)=a_0+a_1x^2+a_2x^4+...+a_n x^(2n)` be a polynomial in a real variable `x` with 0`<` `a_0` `<` `a_1` `<` `a_2` `<......<` `a_n` . The function `P(x)` has a. neither a maximum nor a minimum b. only one maximum c. only one minimum d. only one maximum and only one minimum e. none of these

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

Let P(x) = x^10+ a_2x^8 + a_3 x^6+ a_4 x^4 + a_5x^2 be a polynomial with real coefficients. If P(1)=1 and P(2)=-5 , then the minimum-number of distinct real zeroes of P(x) is

If (18x^2+12x+4)^n = a_0 +a_(1x)+ a_(2x)^2 +......+ a_(2n)x^(2n) , prove that a_r= 2^n3^r ( "^(2n)C_r + "^(n)C_1 "^(2n-2)C_r + "^(n)C_2 "^(2n-4)C_r + ....

Suppose p(x) = a_0 + a_1x + a_2x^2 +…+ a_nx^n . If |p(x)| le |e^(x-1) - 1| le 1 then prove |a1 + 2a2 +...... + n an| ≤ 1.

If (1+x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + "….." + C_(n)x^(n) , then find the value of C_(0)+C_(2)+C_(4)+C_(6)+........ ​ ​

If (1+x+x^2)^n=a_0+a_1x+a_2x^2+.......+a_(2n)x^(2n) , then prove that a_0+a_2+a_4+....+a_(2n)=1/2(3^n+1) .

Let f(x)=a_0+a_1x+a_2x^2+...+a_n x^n and (f(x))/(1-x)=b_0+b_1x+b_2x^2+...+b_n x^n , then a. b_n+b_(n-1)=a_n b. b_n-b_(n-1)=a_n c. b_n/b_(n-1)=a_n d. none of these

If (1+2x+3x^2)^(10)=a_0+a_1x+a_2x^2+.....+a_(20)x^(20),t h e na_1 equals a. 10 b. 20 c. 210 d. none of these

If p(x)=(1+x^2+x^4++x^(2n-2))//(1+x+x^2++x^(n-1)) is a polomial in x , then find possible value of ndot

If (1+x+x^2++x^p)^n=a_0+a_1x+a_2x^2++a_(n p)x^(n p), then find the value of a_1+2a_2+3a_3+ddot+n pa_(n p)dot

If (1+x+x^2)^n=a_0+a_1x+a_2x^2++a_(2n)x^(2n), find the value of a_0+a_3+a_6++ ,n in Ndot

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Investigate for the maxima and minima of the function f(x)=int1^x[2(t...

    Text Solution

    |

  2. The smallest positive root of the equation tanx-x=0 lies in (a)(0,pi/2...

    Text Solution

    |

  3. Let P(x)=a0+a1x^2+a2x^4+...+an x^(2n) be a polynomial in a real variab...

    Text Solution

    |

  4. A cylindrical container is to be made from certain solid material whic...

    Text Solution

    |

  5. Statement 1: If f(0)=0,f^(prime)(x)=ln(x+sqrt(1+x^2)), then f(x) is po...

    Text Solution

    |

  6. Match the items of column I with column II and select the correct opti...

    Text Solution

    |

  7. Find the points at which the function f given by f(x)=(x-5)^4 has loca...

    Text Solution

    |

  8. Find the greatest value of f(x)=1/(2a x-x^2-5a^2)in[-3,5] depending up...

    Text Solution

    |

  9. The set of all values of a for which the function f(x)=(sqrt(a+4)/(1...

    Text Solution

    |

  10. Let f(x)=(x^3-6x^2+12 x-8)e^xdot Statement 1: f(x) is neither maximum...

    Text Solution

    |

  11. Statement 1: The function f(x)=x^4-8x^3+22 x^2-24 x+21 is decreasing f...

    Text Solution

    |

  12. If f is a real function such that f(x) > 0,f^(prime)(x) is continuous ...

    Text Solution

    |

  13. Let f(x)=x^3-3x^2+6AAx in \mathbb{R} and g(x)={m a x :f(t ; x+1lt=tlt=...

    Text Solution

    |

  14. From a fixed point A on the circumference of a circle of radius r , th...

    Text Solution

    |

  15. The lower corner of a leaf in a book is folded over so as to reach the...

    Text Solution

    |

  16. h(x)=3f((x^2)/3)+f(3-x^2)AAx in (-3, 4) where f''(x)> 0 AA x in (-3,4)...

    Text Solution

    |

  17. If 0<x1<x2<x3<pi, then prove that sin((x1+x2+x3)/3)>(sinx1+sinx2+sinx3...

    Text Solution

    |

  18. Prove: sin^2θ+cos^2θ=1

    Text Solution

    |

  19. Prove that (tan^(-1) 1/e)^2+(2e)/ sqrt(e^2+1)<(tan^(-1)e)^2+2/(sqrt(e^...

    Text Solution

    |

  20. If f(x)=x^3+bx^2+cx+d and 0ltb^2ltc then in (-oo,oo)

    Text Solution

    |