First time here? Checkout the FAQ!
+2 votes

Consider the following two statements about the function $f(x)=\left\vert x\right\vert$:

  • 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?

  1. P is true and Q is false.
  2. P is false and Q is true.
  3. Both P and Q are true.
  4. Both P and Q are false.
asked in Calculus by Veteran (56.2k points)   | 251 views

1 Answer

+8 votes
Best answer

ans is A. f(x)=|x| here for all values of x, f(x) exists. therefore it is continuous for all real values of x. 

At x=0, f(x) is not differentiable. Because if we take the left hand limit here, it is negative while the right hand limit is positive.   


answered by Boss (7.4k points)  
selected by
Top Users Jan 2017
  1. Debashish Deka

    8126 Points

  2. sudsho

    5042 Points

  3. Habibkhan

    4706 Points

  4. Vijay Thakur

    4458 Points

  5. Bikram

    4348 Points

  6. saurabh rai

    4212 Points

  7. Arjun

    4010 Points

  8. santhoshdevulapally

    3722 Points

  9. GateSet

    3292 Points

  10. Sushant Gokhale

    3286 Points

Monthly Topper: Rs. 500 gift card

19,122 questions
24,034 answers
20,276 users