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if f: R -> R is a differentiable functio...

if `f: R -> R` is a differentiable function such that`f'(x) > 2f(x)` for all `xepsilonR,` and `f(0) = 1,` then

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Knowledge Check

  • If f:R to R is a twice differentiable function such that f''(x) gt 0" for all "x in R, and f(1/2)=1/2, f(1)=1 then :

    A
    `f'(1) gt 1`
    B
    `f'(1) le 0`
    C
    `1/2 lt f'(1) le 1`
    D
    `0 lt f'(1)= le 1/2`

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