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Let f: R->R satisfying |f(x)|lt=x^2,AAx...

Let `f: R->R` satisfying `|f(x)|lt=x^2,AAx in R` be differentiable at `x=0.` Then find `f^(prime)(0)dot`

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Knowledge Check

  • Let f (x)=xabsx,AAx in R . Then,

    A
    f is derivable at x = 0
    B
    f is not derivable at x = 0
    C
    f is not continuous at x = 0
    D
    None of the above

  • A function f(x) is differentiable at x=c(c in R). Let g(x)=|f(x)|,f(c)=0 then

    A
    g(x) is not differentiable at `x=c`
    B
    for g(x) to be differentiable at c, `f'(c)=0`
    C
    for g(x) to be non-differentiable at `c,f'(c)=0`
    D
    none of these

  • Let f : R to R be a function such that f(x+y) = f(x)+f(y),Aax, y in R. If f (x) is differentiable at x = 0, then

    A
    f(x) is differentiable in a finite interval containing zero
    B
    f(x) is continuous for all ` x in R`
    C
    f'(x) is constant for all ` x in R`
    D
    f(x) is differentiable except at finitely many points

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    Let f(x y)=f(x)f(y)\ AA\ x ,\ y in R and f is differentiable at x=1 such that f^(prime)(1)=1 also f(1)!=0 , f(2)=3 , then find f^(prime)(2) .

    Let f : R rarr R satisfying l f (x) l <= x^2 for x in R, then (A) f' is continuous but non-differentiable at x = 0 (B) f' is discontinuous at x = 0 (C) f' is differentiable at x = 0 (D) None of these

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