Question

Find the equation of the normal to the curve y = |x² – |x|| at x = –2.

Answer 1

The equation of the given curve is

y = |x² – |x||

⇒ y = |x² – (– x)| (since at x = – 2, |x| = –x)

⇒ y = |x² + x|

⇒ y = x² + x (at x = –2, x² + x > 0)

when x = – 2, y = 2

So, the point is (– 2, 2)

Now, dy/dx = 2x + 1

Thus, m = ( dy/dx)_x=–2 = – 3

So, slope of the normal = 1/3

Hence, the equation of the normal is

y – 2 = 1/3(x + 2)

⇒ 3y – 6 = x + 2

⇒ 3y = x + 8