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GATE | GATE-CS-2007 | Question 1

Last Updated : 20 Jun, 2018
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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.


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