Question

$Ifx+4\left|y\right|=6$, then $y$ as a function of $x$ is

• A. $continuousatx=0$
• B. Derivable $x=0$
• C. $\frac{dy}{dx}=\frac{1}{2}forallx$
• D. None of these

Answer 1

Answer: (A), (B)

The correct options are
A $continuousatx=0$
B Derivable $x=0$

$x+4|y|=6$

first draw the graph, $1^{st}$ take $y$ as positive and then as negative we get.

$|y|=\frac{6-4}{4}$

$\Rightarrow$ so, the line is non continuous and non-differentiable only at $x=0$

$\left(i\right)$ continuous at $x=0$

$\left(2\right)$ Derivable at $z=0$

$\left(3\right)$ \dfrac {dy}{dx}=\dfrac {1}{2}$for$x\times (x \neq 6)$