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If the function g(x) = {(ksqrt(x+1) " ...

If the function
`g(x) = {(ksqrt(x+1) " when " 0 le x le 3),(mx + 2 " when " 3 lt x le 5):}`
is differentiable, then the value of (k+m) is -

A

`(10)/(3)`

B

4

C

2

D

`(16)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • If the function f (x)= {{:(e ^(2x) -1",","when " x le 0),(ax+ (bx^(2))/(2)",","when " xgt0):} is differentiable at x=0 then-

    A
    `a=1, b =2`
    B
    `a =2, b=` any value
    C
    `a =2, b=4`
    D
    `a=` any value, `b=4`

  • If f (x) ={{:(x",", "when " 0 lt x lt 1),(2-x",", "when" 1 lt x le 2):} then f'(1) is equal to-

    A
    0
    B
    1
    C
    `-1`
    D
    none of these

  • If f(x)={(x,"when "0le x le 1),(2x-1,"when "x gt 1):} then -

    A
    f(x) is continuous but not differentiable at x=1
    B
    f(x) is discontinuous at x=1
    C
    f(x) is differentiable at x=1
    D
    none of these

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