Home
Class 12
MATHS
Statement I f(x) = |x| sin x is differen...

Statement I f(x) = |x| sin x is differentiable at x = 0.
Statement II If g(x) is not differentiable at x = a and h(x) is differentiable at x = a, then g(x).h(x) cannot be differentiable at x = a

A

A. Statement I is correct, Statement II is also correct, Statement II is the correct explanation of Statement I

B

B. Statement I is correct, Statement II is also correct, Statement II is not the correct explanation of Statement I

C

C. Statement I is correct, Statement II is incorrect

D

D. Statement I is incorrect, Statement II is correct.

Text Solution

Verified by Experts

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

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise EXERCISE 4|3 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1

Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is a. differentiable both at x = 0 and at x = 2 b. differentiable at x = 0 but not differentiable at x = 2 c. not differentiable at x = 0 but differentiable at x = 2 d. differentiable neither at x = 0 nor at x = 2

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

If f(x) = 3(2x + 3)^(2//3) + 2x + 3 , then: (a) f(x) is continuous but not differentiable at x = - (3)/(2) (b) f(x) is differentiable at x = 0 (c) f(x) is continuous at x = 0 (d) f(x) is differentiable but not continuous at x = - (3)/(2)

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):} a. f is continuous at x = 0 b. f is continuous at x = 0 but not differentiable at x = 0 c. f is differentiable at x = 0 d. f is not continuous at x = 0

Let g(x) be the inverse of an invertible function f(x) which is differentiable at x=c . Then g^(prime)(f(x)) equal.

Differentiate sin (x^2 + 5) w.r.t.x.

How many of the function f(x) =|x|, g (x)= |x^2| and h (x) = [x]^3 are not differentiable at x = 0?

Differentiate : x^sin x + (sin x)^x w.r.t x :

Home
Profile