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Prove that sinx+2xgeq(3x(x+1))/pi, AA x ...

Prove that `sinx+2xgeq(3x(x+1))/pi, AA x in [0,pi/2]` (Justify the inequality, if any used).

Text Solution

Verified by Experts

The correct Answer is:
`sinx + 2x ge 3x(x+1)/pi`.
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Knowledge Check

  • If sinx+xge|k|x^(2), AA x in [0,(pi)/(2)] , then the greatest value of k is

    A
    `(-2(2+pi))/(pi^(2))`
    B
    `(2(2+pi))/(pi^(2))`
    C
    can't be determined finitely
    D
    zero

  • If f(x)=2sinx-x^(2) , then in x in [0, pi]

    A
    `f(x)` has no local maximum
    B
    `f(x)` has one local minimum
    C
    `f(x)` has 2 local maxima
    D
    `f(x)` has one local maximum

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