Question

The equation of normal to the curve $y=|x^2-\left|x\right||$ at $x=-2$ is

• A. $3y=2x+10$
• B. $3y=x+8$
• C. $2y=x+6$
• D. $2y=3x+10$

Answer 1

Answer: (B)

$3y=x+8$

$y=\mid x^2-\mid x\mid \mid =(\mid x\mid )(\mid \mid x\mid -1\mid )$

At $x=-2,y=2$

$\frac{dy}{dx}=\frac{\mid x\mid }{x}\mid \mid x\mid -1\mid +\frac{\mid \mid x\mid -1\mid }{\mid x\mid -1}\frac{\mid x^2\mid }{x}$

$(\frac{dy}{dx}{)}_{x=-2}=-1-2=-3$

The equation of normal is $y=\frac{x}{3}+(2+\frac{2}{3})$

$3y=x+8$