Home
Class 12
MATHS
If f(x)={{:(,1,x lt 0),(,1+sin x,0 le x ...

If `f(x)={{:(,1,x lt 0),(,1+sin x,0 le x lt (pi)/(2)):}` then derivative of f(x) x=0

A

1

B

0

C

`infty`

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
D
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise EVALUATION TEST|30 Videos

  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise HIGHER ORDER DERIVATIVES|32 Videos

  • DIFFERENTIAL EQUATIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos

  • INTEGRATION

    TARGET PUBLICATION|Exercise EVALUATION TEST|29 Videos

Similar Questions

Explore conceptually related problems

If f(x)={:{(1+sin x", " 0 le x lt pi//2),(" "1 ", " x lt0):} then show that f(0) =|x| does not exist.

Let f (x) = {{:((1+sin x )",", when, 0 le x lt (pi)/(2)), (" " 1",", when, x lt 0 ):} Show that f ' (0) does not exist.

Knowledge Check

  • If (f) = {{:(1,xlt0),(1+ sinx , 0 lt= x lt=pi//2):} then what is the value of f(x) at x =0 ?

    A
    1
    B
    `-1`
    C
    `oo`
    D
    Does not exist

  • If f(x) = {{:(1, x lt 0),(1 + sinx, for 0 le x lt pi//2):} Then at x=0, the derivative f'(x) is:

    A
    1
    B
    0
    C
    infinite
    D
    does not exist

  • If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

    A
    It has a relative minimum at x = 1
    B
    It has a relative maximum at x =1
    C
    It is not continuous at x = 1
    D
    None of these

    • Similar Questions

    Explore conceptually related problems

    If f(x) {{:( 1,"for " (-pi)/( 2)lt x lt 0 ),( 1+sin x,"for" 0le xlt (pi)/(2) ):},then at x= 0 ,f'(x) -

    Let f(x)={{:(,1+x,"if "x lt 0),(,1+[x]+sin x,0 le x lt pi//2),(,3,x ge pi//2):} Statement-1: F is a continuous on R-[1] Statement-2: The greatest integer function is discontinuous at every integer point.

    Let f (x) = {{:(x ^(3)+x^(2)-10x,,, -1 le x lt 0),( sin x ,,, 0 le x lt (pi)/(2)),( 1+ cos x ,,, (pi)/(2) le x le pi):} then f (x) has:

    f(x) = 1 + 2 sin x + 3 cos^2 x, ( 0 le x lt (2pi)/3) is

    If f (x) = tan ^(-1)sqrt((1 + sin x )/(1 - sin x)), 0 le x le (pi)/(2) then f' ((pi)/(6)) =?

    Home
    Profile