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Let f: R ->R be a differentiable and str...

Let `f: R ->R` be a differentiable and strictly decreasing function such that `f(0)=1` and `f(1)=0`. For `x in R`, let `F(x)=int _0^x(t-2)f(t)dt`

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Knowledge Check

  • Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f '(x) ne 0 for all x in R . If |[f(x)" "f'(x)], [f'(x)" "f''(x)]|= 0 , for all x in R , then the value of f(1) lies in the interval:

    A
    (9, 12)
    B
    (6, 9)
    C
    (0, 3)
    D
    (3,6)

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