What is the equation of the line normal

Darian Silva

Darian Silva

Answered question

2022-04-10

What is the equation of the line normal to f(x)=(3x-1)(x+4) at x=-3?

Answer & Explanation

granfury90210birm

granfury90210birm

Beginner2022-04-11Added 10 answers

Take the derivative of the equation to find the slope of the tangent, and then the slope of the normal is the negative inverse.
First expand the equation to simplify getting the derivative:
f(x)=(3x2+11x4)
f'(x)=6x+11
At the point x=-3 the slope is 6(-3)+11=-7
The slope is -7, therefore the slope of the normal is 17
The equation of the normal is therefore y=17x+c
At the point x=-3 the original expression gives y=27-33-4=-10
Plugging this back into the normal gives c=1017(3)=677
The normal equation is therefore y=17x677 or
7y=x-67

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