What is the equation of the normal line

Frances Simon

Frances Simon

Answered question

2022-04-08

What is the equation of the normal line of f(x)=-4x-10 at x=-2?

Answer & Explanation

Ouhamiptkg

Ouhamiptkg

Beginner2022-04-09Added 18 answers

The normal line at x=-2 is the line perpendicular to the tangent line at this point. The slope of the tangent line is simply the derivative evaluated at x=-2.
f'(-2)=-4
The slope of the line normal to the tangent line is the negative reciprocal of this i.e.
m=14. Now we have a slope, but we still need a point to write the line. So, evaluate the function at x=-2.
f(-2)=-4(-2)-10=-2
We now have the slope and a point, so use point slope form to acquire the equation of the normal line.
y+2=14(x+2)
or
y=x432

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