What is the equation of the normal line

Breanna Mcclure

Breanna Mcclure

Answered question

2022-04-10

What is the equation of the normal line of f(x)=x3+3x2+7x1 at x=-1?

Answer & Explanation

posciad48o

posciad48o

Beginner2022-04-11Added 15 answers

Explanation:
f(x)=x3+3x2+7x1
The gradient function is the first derivative
f(x)=3x2+6x+7
So the gradient when X=-1 is 3-6+7=4
The gradient of the normal , perpendicular, to the tangent is 14
If you are not sure about this draw a line with gradient 4 on squared paper and draw the perpendicular.
So the normal is y=14x+c
But this line goes through the point (-1,y)
From original equation when X=-1 y=-1+3-7-1=6
So 6=141+c
C=234

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