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The left hand derivative of the function...

The left hand derivative of the function `y = f(x) ` at x = a is Lf' (a) =

A

`underset(h to 0+)lim (f(a+h)-f(a))/(h)`

B

`underset(h to 0-)lim (f(a+h)-f(a))/(h)`

C

`underset(h to 0)lim (f(a+h)-f(a))/(h)`

D

none of these

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The correct Answer is:
B
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Knowledge Check

  • The right hand derivative of the function y = f(x) at x = a is Rf' (a) =

    A
    `underset(h to 0+1)lim (f(a+h)-f(a))/(h)`
    B
    `underset(h to 0)lim (f(a+h)-f(a))/(h)`
    C
    `underset(h to 0-1)lim (f(a+h)-f(a))/(h)`
    D
    none of these

  • The derivative of the function y = f (x) at x = a exists if Rf'(a) and Lf'(a) both exist and if -

    A
    `Rf'(a)=0`
    B
    `Lf'(a)=0`
    C
    `Rf'(a)=Lf'(a)`
    D
    `Rf'(a) neLf'(a)`

  • The derivative of the function f(x)=3|x+2| at the point, x = -3 is -

    A
    -3
    B
    3
    C
    0
    D
    does not exist

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