Question

If x + 4 |y| = 6y, then y as a function of x is –

• A. Not continuous at x = 0
• B. Not defined for all real x
• C. $\frac{dy}{dx}$ = $\frac{1}{2}$ for x > 0
• D. Derivable at x = 0

Answer 1

Answer: (C)

$\frac{dy}{dx}$ = $\frac{1}{2}$ for x > 0

Answer 2

x + 4|y| = 6y

y > 0 y £ 0

x + 4y = 6y x – 4y = 6y

y = x/2 x = 10y

y = x/10

y = $\left\{ \begin{matrix} x/2 & x > 0 \\ x/10 & x \leq 0 \end{matrix} \right.\$

Continuous everywhere not differentiable at x = 0,

For x > 0, $\frac{dy}{dx}$= $\frac{1}{2}$