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Find the values of parameter a for which...

Find the values of parameter a for which the function.
`y=ax^(3)+3x^(2)+(2a+1)x+1000`
is strictly decreasing for all real values of x.

Answer

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Knowledge Check

  • The value of a for which the function (a+2)x^(3) - 3ax^(2) + 9ax -1 decreases monotonically throughout for all real values of x , are-

    A
    `a lt -2`
    B
    `a gt -2`
    C
    ` -3 lt a lt 0 `
    D
    ` a le -3 `
  • If f(x)= x^(3) + ax^(2) + bx + c is an increasing function for all real values of x then-

    A
    ` a^(2) gt 3b `
    B
    ` a^(2) lt 3b `
    C
    ` b^(2) gt 3a `
    D
    ` b^(2) lt 3a `
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    Find the value of a for which the function (a+2)x^3-3a x^2+9a x-1 decreases montonically for all real xdot

    Find the condition so that the function f(x)=x^(3)+ax^(2)+bx+c is an increasing function for all real values of x.

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