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+3 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 (67.5k points) | 631 views

1 Answer

+9 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 (8.4k points)
selected by
at x= 0, Left hand derivative is not equal to right hand derivative. So it is not differentiable.

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