Home
Class 11
MATHS
Check whether the function f (x) = {{:(3...

Check whether the function `f (x) = {{:(3 + x if x ge 0), ( 3-x if x lt 0):}` is differentiable at `x =0.`

Text Solution

Verified by Experts

The correct Answer is:
`x=0`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIATION

    AAKASH SERIES|Exercise ADVANCED ANALYTICAL SOLVED EXAMPLES |6 Videos

  • DIFFERENTIATION

    AAKASH SERIES|Exercise EXERCISE -4.1|10 Videos

  • DIFFERENTIATION

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTIONS |26 Videos

  • CONTINUITY

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTIONS|34 Videos

  • DIFFRENTATION

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (PRACTICE SHEET (ADVANCED)) (Integer Type Questions)|5 Videos

Similar Questions

Explore conceptually related problems

Show that the functions f (x) = x ^(3) sin ((1)/(x)) for x ne 0, f (0) =0 is differentiable at x =0.

If the function f(x) = {(x, if 0 le x le 2),(2, if x ge 2):} derivable at 2? Justify.

Knowledge Check

  • f(x) = {{:(4-3x " if " x le 0),(2a + x " if " x ge 0):} is continuous at x = 0 then a =

    A
    1
    B
    2
    C
    3
    D
    4

    • Similar Questions

    Explore conceptually related problems

    Show that the function f (x) = (x)/(1 + |x| ) , x in R, is differentiable at x =0. Hence find f '(0).

    Show that the function f (x) = {{:((x -1 ) sin ((1)/(x -1)) "for" x ne a), (0 " ""for" x =a):} is not differentiable at x =a.

    Show that the function f given by f(x)= {{:(x^3+3," if "x ne 0),(1," if "x=0):} is not continuous at x=0.

    Discuss the continuity of the function f given by {{:(x," if "x ge 0),(x^2," if "x lt 0):} .

    Show that the function f (x) = x ^(p) sin ((1)/(x)) x , ne 0, f (0) =0 is continuous but not differentiable at x=0 if 0 lt p le 1.

    Cheak whether the following function is differentiable at zero f(x)={{:(3+x"if" xge0),(3-x"if" xlt0):}

    Check the continuity of the function ‘f defined by f(x)={{:(cos x,if x ne 0),(1 ,if x=0):} at x=0

    Home
    Profile