Which of the following statements is not true?

  • A
    $A$ polynomial function is always continuous.
  • B
    $A$ continuous function is always differentiable.
  • C
    $A$ differentiable function is always continuous.
  • D
    $e^x$ is continuous for all $x$.

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Let $f(x) = x |\sin x|$,$x \in R$. Then,

If $f(x)=|x|+|\sin x|$ for $x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$,then its left hand derivative at $x=0$ is

The values of $x$ at which the real-valued function $f(x) = 7|2x + 1| - 19|3x - 5|$ is not differentiable are:

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