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If f(x)=ax^(3)-9x^(2)+9x+3 is monotonica...

If `f(x)=ax^(3)-9x^(2)+9x+3` is monotonically increasing in each interval, then `a ge k`, find k.

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Knowledge Check

  • If f(x)= kx^(3) - 9x^(2) + 9x + 3 is an increasing function then-

    A
    `k lt 3 `
    B
    ` k le 3 `
    C
    `k gt 3 `
    D
    k is indeterminate

  • The function f(x)=cos x - 2ax is monotonically decreasing when-

    A
    `a lt (1)/(2)`
    B
    `a gt (1)/(2)`
    C
    `a lt 0`
    D
    `a gt 0`

  • If f(x) = x^(3) - 6x^(2) + 9x +3 be a decreasing function, then x lies in-

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

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