What is the equation of the line normal

Magdalena Warren

Magdalena Warren

Answered question

2022-04-08

What is the equation of the line normal to f(x)=lnxx3 at x=1?

Answer & Explanation

Austin Sherman

Austin Sherman

Beginner2022-04-09Added 12 answers

First find the gradient of f(x) by differentiating. Then if the gradient is m the slope
of the normal is 1m
The rest of the equation can be found by substituting in the values at the given point.
f(x)=lnxx3
f(x)=1x3x2
At x=1, m=13.12=2
Therefore the slope of the normal is 12
Going back to the original expression
f(1)=ln(1)13=01=1
The equation of the normal is y=mx+c
At the given point 1=12(1)+c
c=32
The equation of the normal is
y=12x32
or 2y=x-3

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