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 (64.4k points)   | 540 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 (8.2k points)  
selected by
at x= 0, Left hand derivative is not equal to right hand derivative. So it is not differentiable.

Top Users Sep 2017
  1. Habibkhan

    6334 Points

  2. Warrior

    2202 Points

  3. Arjun

    2150 Points

  4. nikunj

    1980 Points

  5. manu00x

    1726 Points

  6. SiddharthMahapatra

    1718 Points

  7. Bikram

    1706 Points

  8. makhdoom ghaya

    1650 Points

  9. A_i_$_h

    1518 Points

  10. rishu_darkshadow

    1512 Points

25,979 questions
33,554 answers
31,011 users