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If f(x) = {(px + q, :x le 2),(x^2 - 5x +...

If `f(x) = {(px + q, :x le 2),(x^2 - 5x + 6, : 2 < x < 3),(ax^2 + bx + 1, : x ge 3):}`
is differentiable everywhere, then `|p| + |q| + |1/a| + |1/b|` is equal to

A

`(71)/(10)`

B

`(51)/(10)`

C

`(33)/(5)`

D

`(31)/(5)`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If f(x)={{:(2x^(2)+3,,,xge3),(ax^(2)+bx+1,,,xle3):} is differentiable everywhere, then (a)/(b^(2)) is equal to

    A
    5
    B
    `(7)/(3)`
    C
    1
    D
    `(16)/(9)`

  • If the function f(x)={{:(-x",",,x lt 1),(a+cos^(-1)(x+b),,1 le x le 2):} is differentiable at x = 1, then (a)/(b) is equal to

    A
    `(pi+2)/(2)`
    B
    `(pi-2)/(2)`
    C
    `(-pi-2)/(2)`
    D
    `-1-cos^(-1)(2)`

  • If the function f(x)={{:(,-x,x lt 1),(,a+cos^(-1)(x+b),1 le xle 2):} is differentiable at x=1, then (a)/(b) is equal to

    A
    `(-pi-2)/(2)`
    B
    `-1-cos^(-1)`
    C
    `(pi)/(2)+1`
    D
    `(pi)/(2)-1`

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