Home
Class 12
MATHS
If f(x) = {{:(|x-1|([x]-x)",",x ne 1),(0...

If `f(x) = {{:(|x-1|([x]-x)",",x ne 1),(0",",x = 1):}`, then

A

`f'(1^(+)) = 0`

B

`f'(1^(-)) = 0`

C

`f'(1^(-)) = - 1`

D

f(x) is differentiable at x = 1

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

f(x) = {((|x|)/(x)",","if" x ne 0),(0",","if" x= 0):}

A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0):} , then f(x) is(a) continuous at x = 0 ,(b) continuous at x = 1 (c)differentiable at x = 0

Evaluate lim_(xrarr0)f(x)," where "f(x)={{:((|x|)/(x)",",x ne0),(0",",x=0):}

f(x)= {((|sin x|)/(x)",",x ne 0),(1",",x=0):} Examine the continuity of f(x), x= 0

If f(x)= {(x",",x in {0, 1}),(1",",x ge 1):} then, ……

f(x)= {((1)/(e^(4x) + 1)",",x ne 0),(0",",x = 0):} Examine the continuity of f(x) at x= 0

Let f(x)={{:(x sin.(1)/(x)",",x ne0),(0",",x=0):}} and g(x)={{:(x^(2)sin.(1)/(x)",", x ne 0),(0",", x=0):}} Discuss the graph for f(x) and g(x), and evaluate the continuity and differentiabilityof f(x) and g(x).