Home
Class 12
MATHS
If [(4a^2,4a, 1),(4b^2, 4b,1), (4c^2, 4c...

If `[(4a^2,4a, 1),(4b^2, 4b,1), (4c^2, 4c, 1)] [(f(-1)),(f(1)),(f(2))] = [(3a^2 + 3a) ,(3b^2 + 3b) ,(3c^2 + 3c)]`,
`f(x)` is a quadratic function and its maximum value occurs at a point V. A is a point of intersection of `y = f(x)` with x-axis and point B is such that chord AB subtends a right angled at V. Find the area enclosed by `f(x)` and chord AB.

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    CENGAGE PUBLICATION|Exercise All Questions|674 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE PUBLICATION|Exercise Subjective Type|2 Videos

Similar Questions

Explore conceptually related problems

Find the points of inflection for (a) f(x)=sinx (b) f(x)=3x^4-4x^3

A straight line AB intersects the y-axis at B and the perpendicular to AB at B intersects the x-axis at C . If the equation of the straight line AB is (x)/(3)-(y)/(4)=-1 find the coordinates of the points C.

If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c , then (a) f(x) is an even function (b) f(x) is a bounded function (c) the range of f(x) is (0,1) (d) f(x) has two points of extrema

If the area bounded by the curve y=f(x), x-axis and the ordinates x=1 and x=b is (b-1) sin (3b+4), then find f(x).

AB is a chord of x^2 + y^2 = 4 and P(1, 1) trisects AB. Then the length of the chord AB is (a) 1.5 units (c) 2.5 units (b) 2 units (d) 3 units

If the domain of the function f(x) = sqrt(3 cos^(-1) (4x) - pi) is [a, b] , then the value of (4a + 64b) is ___

If f(x)=|[(x-a)^4, (x-a)^3, 1] , [(x-b)^4, (x-b)^3,1] , [(x-c)^4, (x-c)^3,1]| then f'(x)=lambda|[(x-a)^4,(x-a)^2,1] , [(x-b)^4, (x-b)^2, 1] , [(x-c)^4, (x-c)^2,1]| . Find the value of lambda

The lines joining the origin to the point of intersection of The lines joining the origin to the point of intersection of 3x^2+m x y=4x+1=0 and 2x+y-1=0 are at right angles. Then which of the following is not a possible value of m ? -4 (b) 4 (c) 7 (d) 3

If f(x)=ax^(2)+bx+c and f(0) = 2, f(1) = 1, f(4) = 6, then find the valuse of a, b and c.

Give f(x) = a + b(x - 10) + c(x - 1)(x - 2), f(1) = 7, f(2) = 17 and f(3) = 35, determine the coefficients a, b and c

CENGAGE PUBLICATION-APPLICATION OF INTEGRALS-All Questions
  1. Find the area bounded by the curve x^(2) = 4y and the line x = 4y - 2.

    Text Solution

    |

  2. The area of the region bounded by the curves y=x^(2),y=|2-x^(2)| and y...

    Text Solution

    |

  3. If [(4a^2,4a, 1),(4b^2, 4b,1), (4c^2, 4c, 1)] [(f(-1)),(f(1)),(f(2))] ...

    Text Solution

    |

  4. If f(x) is a function such that f'(x)=(x-1)^2 (4-x), then

    Text Solution

    |

  5. The area bounded by the curves y=|x|-1a n dy=-|x|+1 is 1 sq. units (b)...

    Text Solution

    |

  6. If the area bounded by the curve y=f(x), x-axis and the ordinates x=1 ...

    Text Solution

    |

  7. The area bounded by the parabolas y=(x+1)^2 and y=(x-1)^2a n dy=(x-1)^...

    Text Solution

    |

  8. The area bounded by the curves y=sqrt(x),2y+3=x , and x-axis in the 1s...

    Text Solution

    |

  9. Find the area bounded by y=tan^(-1)x , y=cot^(-1)x ,and y-axis in the...

    Text Solution

    |

  10. the equation to the director circle of (x^2)/6+(y^2)/4=1 is

    Text Solution

    |

  11. Find the area bounded by y=loge x , y=-loge x ,y=loge(-x),a n dy=-loge...

    Text Solution

    |

  12. The area of region for which 0 lt y lt 3 - 2x-x^2 and x gt 0 is

    Text Solution

    |

  13. The area common to regions x^2+y^2-2xlt=0 and ygeq sin (pix/2)

    Text Solution

    |

  14. Draw the rough sketch of the curve y=x^(4)-x^(2).

    Text Solution

    |

  15. f(x) is a continuous and bijective function on Rdot If AAt in R , the...

    Text Solution

    |

  16. Find the continuous function f where (x^4-4x^2)lt=f(x)lt=(2x^2-x^3) su...

    Text Solution

    |

  17. Find the area bounded by the curves y=-x^2+6x-5,y=-x^2+4x-3, and the s...

    Text Solution

    |

  18. Find the value of a where (a >2) for which the reciprocal of the area ...

    Text Solution

    |

  19. if A1,A2,A3,....A100 are set of A1 sub A2 sub A3 sub A4.....sub A100 n...

    Text Solution

    |

  20. Draw the rough sketch of y^2+1=x ,\ xlt=2. Find the area enclosed by t...

    Text Solution

    |