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The set of values of p for which the poi...

The set of values of p for which the points of extremum of the function, `f(x) = x^3 -3px^2 + 3 (p^2 -1)x + 1` lin in the interval `(-2,4)` is

A

`(-3,5)`

B

`(-3 , 3)`

C

`(-1,3)`

D

`(-1,4)`

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • The set of values of p for which the points of extrema of the function, f (x) = x ^(3) - 3p x ^(2) + 3 ( p ^(2) -1) x + 1 lie in the interval (-2,4) is:

    A
    `(-3,5)`
    B
    `(-3,3)`
    C
    `(-1,3)`
    D
    `(-1,5)`

  • The function f(x) = 2x^(3) + 3x^(2) -12 x + 1 decreases in the interval

    A
    (2,3)
    B
    (1,2)
    C
    `(-2,1)`
    D
    `(-3,-2)`

  • The value of a for which all extremum of function f(x)=x^(3)+3ax^(2)+3(a^(2)-1)x+1 , lie in the interval (2, 4) is

    A
    `(3,4)`
    B
    `(-1,3)`
    C
    `(-3, -1)`
    D
    none of these

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