Question

A line perpendicular to another line or to a tangent line is called a normal line. Find an equation of the line perpendicular to the line that is tangent to the following curve at the given point P. y = x ² – 3x; P(5,10)

Answer 1

Hi,

Explanation:

`curve:\ y=x^2-3x\\y'=2x-3\\\\Slope\ of\ the\ tangent\ \ at\ P:\ y'(5)=2*5-3=7\\\\Slope\ of\ the\ normal\ \ at\ P:\ m*7=-1\ = > \ m=(-1)/(7) \\\\Equation\ of\ the\ normal\ at\ P:\ y-10=(-1)/(7)(x-5)\\\\or\ y=(-x)/(7) +(75)/(7)`