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Let f(x)={{:(xe^(ax)",", x le0),(x+ax^2-...

Let `f(x)={{:(xe^(ax)",", x le0),(x+ax^2-x^3",",x gt 0):}` where a is postive constant . Find the interval in which f'(X) is increasing.

Text Solution

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The correct Answer is:
`(-2/a, 0)cup(0,a/3)`
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Knowledge Check

  • Let f(x)={{:(xe^(ax) "," x le 0 ),(x+ax^2-x^3 "," x gt 0 ):} ,where is a positive constant .Then the interval in which f' (x ) is increasing is

    A
    `(0,a/3)`
    B
    (-2 /a,0)
    C
    (-2/a,a/3)
    D
    non of these

  • Let f(x)=(3x-7)x^(2/3) . The interval in which f(x) is increasing.

    A
    `(0,14/15)`
    B
    `(-oo,0)uu(14/15,oo)`
    C
    `(-oo,14/15)`
    D
    `(0,oo)`

  • Let f(x) ={{:( xe^(x), xle0),( x+x^(2)-x^(3), xgt0):} then the correct statement is

    A
    f is continuous and differentiable for all x,
    B
    f is continuous but not differentiable ata x=0
    C
    f is continuous and differentiable for all x.
    D
    f ' is continuous but not differentiable at x=0.

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