Equation of the line normal to function f(x) = (x

Equation of the line normal to function f(x) = (x – 8)^{2 / 3} + 1 at P(0, 5) is

Given, f(x) = (x – 8)^{2 / 3} + 1
m_normal × m_tangent = – 1

where, m_tangent =	dy	and m_normal =	-1
	dx		(dy / dx)

	dy	=	df(x)	=	2	(x – 8)^{-1 / 3}
	dx		dx		3

m_normal =	-3	(x – 8)^{-1 / 3} or [m_normal]_{0 , 5} = 3
	2

∴ Equation of normal is, (y – y₁) = mnormal (x – x₁)
or (y – 5) = 3 (x – 0) or y = 3x + 5