Home
Class 12
MATHS
If f(x)=(x-1)(x-2)(x-3)(x-4), show that...

If `f(x)=(x-1)(x-2)(x-3)(x-4)`, show that the equation f'(x)=0 has three roots `alpha, beta` and `gamma` where `1 lt alpha lt 2, 2 lt beta lt 3` and `3 lt gamma lt 4`.

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Multiple Correct Answers Type)|5 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Integer Answers Type)|5 Videos

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3B (Very Short Answer Type Questions)|33 Videos

  • DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE

    CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

If f(x)= int e^(x)(x-1)(x-2)dx , then show that f(x) is a decreasing function 1 lt x lt 2 .

3(1-x) lt 2(x+4)

If 0 lt alpha lt beta lt (pi)/(2) , prove that, tan alpha-tan beta lt alpha-beta .

Prove that the function f(x)=x^(3)-x^(2) is neither increasing nor decreasing in -2/3 lt x lt 2/3 .

Evaluate int_(0)^(pi)(x dx)/(1+cos alpha sin x) ,where 0lt alpha lt pi .

For 2 lt x lt 4 , find the values of |x|.

If alpha,beta are roots of x^2-3x+a=0 , a in R and alpha <1< beta then find the value of a.

If 0 lt x lt pi/2 , show that, sin x lt x lt tan x

If alpha,beta,gamma are the roots of the equation x^3+x+1=0 , then the value of alpha^3+beta^3+gamma^3 is.

Show that the function f(x) =sin^(4)x+cos^(4)x is increasing in (pi)/(4) lt x lt (3pi)/(8) .

CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3B (Short Answer Type Questions)
  1. Let f(x)=4x^(3)+x^(2)-4x-1. The equation f(x)=0 has roots 1 and (-(1)/...

    Text Solution

    |

  2. If f(x) is a polynomial, show that between two roots of the polynomial...

    Text Solution

    |

  3. If f(x)=(x-1)(x-2)(x-3)(x-4), show that the equation f'(x)=0 has thre...

    Text Solution

    |

  4. Show that the equation e^(x-1)+x-2=0 has no real root which is less t...

    Text Solution

    |

  5. If the function f(x)=x^(3)+ax^(2)-bx+4 defined in -2 le x le 2 satisfi...

    Text Solution

    |

  6. Using Rolle's theorem, find the point on the curve y=x(x-4), x in [0...

    Text Solution

    |

  7. Using Rolle's theorem, find the point on the curve f(x)=(1-cosx)" i...

    Text Solution

    |

  8. At what point is the tangent to the curve f(x)=log x parallel to the c...

    Text Solution

    |

  9. In the mean value theorem f(b)-f(a)=(b-a)f'(c ), (a lt c lt b)," if " ...

    Text Solution

    |

  10. In the mean value theorem, f(a+h)=f(a)+hf'(a+theta h) (0 lt theta lt 1...

    Text Solution

    |

  11. In the mean value theorem, f(x+h)=f(x)+hf'(x+theta h)(0 lt theta lt 1...

    Text Solution

    |

  12. Using Lagrange's mean value theorem prove that, e^(x) gt 1 +x

    Text Solution

    |

  13. Using Lagrange's mean value theorem prove that, log (1+x) lt x ("wh...

    Text Solution

    |

  14. Using Lagranges mean value theorem, prove that |cosa-cosb|<=|a-b|dot

    Text Solution

    |

  15. Using Lagrange's mean value theorem prove that, (b-a)sec^(2)a lt ta...

    Text Solution

    |

  16. If f(x)=(1)/(x), then find the value of theta in the mean value theor...

    Text Solution

    |

  17. Using Lagrange's mean value theorem, find a point on the curve y=sqrt(...

    Text Solution

    |

  18. Using Lagrange's mena value theorem, find a point on the curve y=x^(2)...

    Text Solution

    |