Question

Tangent and Normal line?

Answer 1

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Answer 2

I already got the tangent, just don't know what a normal line is.

Answer 3

A normal line is the line through the point of contact of the tangent but perpendicular

Answer 4

normal line is the line that is perpendicular to the tangent line that passes through the same point of tangency

Answer 5

Slope of tangent=>\[\frac{dy}{dx}=4(x e^x+e^x)=>4e^x(x+1)\]
Slope of Normal=>
\[\frac{dy}{dx}=\frac{-1}{4e^x(x+1)}\]
since m1 m2 =-1..
At (0,0)
\[\frac{dy}{dx}]_{0,0}=>\frac{-1}{4}\]

Answer 6

\[\Large y-y_1=m(x-x_1)\]
x=0
y=0