How do you find the equation of the tangent line

m1cadc

m1cadc

Answered question

2022-02-10

How do you find the equation of the tangent line and normal line to the curve at the given point y=(1+2x)2, (1,9)?

Answer & Explanation

Ethen Welch

Ethen Welch

Beginner2022-02-11Added 11 answers

Explanation:
the slope of tangent at (1,9) is (1+2x)*2 by normal differentiation
at x=1 the slope value is 12
let the equation of tangent is y=mx+c
substituiting points
9=12+c
c=-3
equation of tangent is y=12x-3
for normal line
slope =-1/12
from the line formula y=mx+c
substituiting points
9=-1/12+c
c=109/12
equation is
12y = 109-x

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