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Give a function on the interval [-2,+2] ...

Give a function on the interval [-2,+2]
`f(x)={{:(,x^(2)+2,if ,-2 le x lt 0),(,-x^(2)+2, if ,0 le x le 2):}` Is there a point on this closed interval at which f(x)=0?

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Knowledge Check

  • If f(x)={{:(,(x^(2))/(2),0 le x lt 1),(,2x^(2)-3x+(3)/(2),1 le x le 2):} then,

    A
    f, f' and f'' are continuous in [0,2]
    B
    f and f' are continuous in [0,2] whereas f'' is continuous in `[0,1] uu (1,2]`
    C
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    D
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  • If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

    A
    It has a relative minimum at x = 1
    B
    It has a relative maximum at x =1
    C
    It is not continuous at x = 1
    D
    None of these

  • If f(x)={:{(x", for " 0 le x lt 1/2),(1-x", for " 1/2 le x lt 1):} , then

    A
    `underset(x rarr 1^(-)/2) lim f(x)=(-1)/(2)`
    B
    `underset(x rarr 1^(+)/2)lim f(x)=(-1)/(2)`
    C
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    D
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