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In which of the following cases, the fun...

In which of the following cases, the function f(x) has vertical tangent at x = 0 ?
(i) `f(x)=x^(1//3)`

Answer

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Knowledge Check

  • The function f(x)=|x| has:

    A
    only one minima
    B
    only one maxima
    C
    no maxima or minima
    D
    None of these.

  • The function f(x)=x+(4)/(x) has :

    A
    a local maxima at x = 2 and a local minima at x = -2
    B
    local minima at x = 2 and a local maxima at x = -2
    C
    absolute maxima at x = 2 and absolute minima at x = -2
    D
    absolute minima at x = 2 and absolute maxima at x = -2.

  • The function f(x)=x^(3)-3x is :

    A
    increasing in `(-oo, -1)cup [1, oo)` and decreasing in (-1, 1)
    B
    decreasing in `(-oo, -1) cup [1, oo)` and increasing in (-1, 1)
    C
    increasing in `(0, oo)` and decreasing in `(-oo, 0)`
    D
    decreasing in `(0, oo)` and increasing in `(-oo, 0)`.

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    Find the range of each of the following functions. (i) f(x)=2-3x, x in R, x gt 0 (ii) f(x)=x^(2)+2, x is a real number. (iii) f(x) = x, x is a real number

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