Skip to content
Related Articles

Related Articles

Improve Article

GATE | GATE-CS-2007 | Question 1

  • Difficulty Level : Easy
  • Last Updated : 20 Jun, 2018

Consider the following two statements about the function f(x)=|x|

P. f(x) is continuous for all real values of x
Q. f(x) is differentiable for all real values of x 

Which of the following is TRUE?

(A) P is true and Q is false.
(B) P is false and Qis true.
(C) Both P and Q are true
(D) Both P and Q are false.

Answer: (A)

Explanation: A function is continuous if for every value of ‘x’, we have a corresponding f(x). Here, for every x, we have f(x) which is actually the value of x itself, without the negative sign for x < 0.

But, the given function is not differentiable for x = 0 because for x < 0, the derivative is negative and for x > 0, the derivative is positive. So, the left hand derivative and right hand derivative do not match.


Hence, P is correct and Q is incorrect.
Thus, A is the correct option.

Please comment below if you find anything wrong in the above post.

Quiz of this Question

Attention reader! Don’t stop learning now.  Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.

Learn all GATE CS concepts with Free Live Classes on our youtube channel.

My Personal Notes arrow_drop_up
Recommended Articles
Page :