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Let f(x)={x^3-x^2+10 x-5,xlt=1-2x+(log)2...

Let `f(x)={x^3-x^2+10 x-5,xlt=1-2x+(log)_2(b^2-2),x >1` Find the values of `b` for which `f(x)` has the greatest value at `x=1.`

A

`1ltble2`

B

`b={12}`

C

`b in(-oo,-1)`

D

`[-sqrt(130)-sqrt(2)]cup(sqrt(2),(sqrt(130))`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • Let f(x)={{:( x^3 - x^2 + 10 x -5, x le 1),(-2x + log_2 ( b^2-2) ,x gt 1):} the set of values of b for which f (x) have greatest value at x = 1 is given by

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    ` 1 le b le 2`
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    ` b = {1,2}`
    C
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    D
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  • Let f(x)={{:(3x^2-2x+10, x lt 1),(-2,x gt 1):} The set of values of b for which f(x) has greatest value at x=1 is

    A
    `(-6,-2)`
    B
    (2,6)
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    `(-6,-2)cup (2,6)`
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  • Let f (x) = {{:( x^(3) - x^(2) + 10 x- 5 , "," , x le 1), ( -2x + log _(2) (b^(2) - 2) , "," , x gt 1):} the set of values of b for which f(x) has greatest value at x = 1 is given by

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    B
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