Home
Class 12
MATHS
If f(x)={'x^2(sgn[x])+{x},0 <= x <= 2' ...

If `f(x)={'x^2(sgn[x])+{x},0 <= x <= 2' 'sin x+|x-3| ,2 < x< 4 ,` (where[.] & {.} greatest integer function & fractional part functiopn respectively ), then -

Option 1. f(x) is differentiable at x = 1
Option 2. f(x) is continuous but non-differentiable at x
Option 3. f(x) is non-differentiable at x = 2
Option 4. f(x) is discontinuous at x = 2

A

f(x) is differentiable at x=1

B

f(x) is continuous but non - differentiable at x=1

C

f(x) is non-differnentiable at x=2

D

f(x) is discontinuous at x=2

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x)={'x^2(sgn[x])+{x},0 Option 1. f(x) is differentiable at x = 1 Option 2. f(x) is continuous but non-differentiable at x = 1 Option 3. f(x) is non-differentiable at x = 2 Option 4. f(x) is discontinuous at x = 2

If f(x) = x^(3) sgn (x), then A. f is differentiable at x = 0 B. f is continuous but not differentiable at x = 0 C. f'(0^(-)) = 1 D. None of these

Show that the function f(x)=|x-2| is continuous but not differentiable at x=2.

Show that the function f(x) =x^2 is continuous and differentiable at x=2.

If f(x)=sin^(-1) ((2x)/(1+x^2)) then f(x) is differentiable on

The contrapositive of statement: If f(x) is continuous at x=a then f(x) is differentiable at x=a

If g(x)=(2h(x)+|h(x)|)/(2h(x)-|h(x)|) where h(x)=sinx-sin^n x ,n in R^+, the set of positive real numbers, and f(x)={[g(x)],x(0,pi/2)uu(pi/2,pi) and 3,x=pi/2 where [.] denotes greatest integer function. Then (a) f(x) is continuous and differentiable at x=pi/2, when 0ltnlt1 (b) f(x) is continuous and differentiable at x=pi/2, when ngt1 (c) f(x) is discontinuous and non differentiable at x=pi/2,for0ltnlt1 (d) f(x) is continuous but not differentiable at x=pi/2, when ngt1

If f(x)=x^3(sgn [x] + {x}):0le xlt2, cosx+|x-2| ; 2 le x le pi Where [.], {.} and sgn (.) represents the greatest integer, the fractional part and signmum function respectively A. f(x) is differentiable at x = 1 B) f(x) is continuous but non-differentiable at x = 1 C) f(x) is discontinuous at x= 2 D) f(x) is non-differentiable at x =2

Let f(x)={{:(,x^(n)sin\ (1)/(x),x ne 0),(,0,x=0):} Then f(x) is continuous but not differentiable at x=0 . If

Let f(x) ={{:( xe^(x), xle0),( x+x^(2)-x^(3), xgt0):} then the correct statement is (a) f is continuous and differentiable for all x (b) f is continuous but not differentiable at x=0 (c) f is continuous and differentiable for all x . (d) f ' is continuous but not differentiable at x=0