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Let f(x)=4x^(3)+x^(2)-4x-1. The equation...

Let `f(x)=4x^(3)+x^(2)-4x-1`. The equation f(x)=0 has roots 1 and `(-(1)/(4))`. Find the root of f'(x)=0 mentioned in Rolle's theorem.

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2)`
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Knowledge Check

  • If the function f(x) is defined by f(x)=(x(x+1))/(e^(x)) in [-1, 1], then the values of c in Rolle's theorem is -

    A
    `(1-sqrt(3))/(2)`
    B
    `(1-sqrt(3))/(4)`
    C
    `(1-sqrt(5))/(2)`
    D
    `(1-sqrt(5))/(4)`

  • Let a function f(x) be defined by f(x)=x^(3)-2x in [0, sqrt(2)] , then the value of c in Rolle's theorem is -

    A
    -1
    B
    1
    C
    `(1)/(2)`
    D
    none of these

  • If the function f(x)=4x^(3)+ax^(2)+bx-1 satisfies all the conditions of Rolle's theorem in -(1)/(4) le x le 1 and if f'((1)/(2))=0 , then the values of a and b are -

    A
    `a=2, b=3`
    B
    `a=1,b=-4`
    C
    `a=-1, b=4`
    D
    `a=-4, b=-1`

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