A line perpendicular 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^2-4x; P(7,21)

Question

The equation of the normal line at P(7,21) is

Answer 1

f(x)=x²-4x

f '(x)=2x-4

f '(7)=10=m

m₂=-1/m = -1/10 Slope of normal line

Normal line:

y-21 = m₂(x-7) = -(x-7)/10

y = -x/10 +21.7

Answer 2

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Answer 3