What is the equation of the line that

Harrison Reeves

Harrison Reeves

Answered question

2022-04-08

What is the equation of the line that is normal to f(x)=(x3)22x2 at x=-1?

Answer & Explanation

cm1mmeboulbes21e1

cm1mmeboulbes21e1

Beginner2022-04-09Added 8 answers

Explanation:
Lets differentiate the function to find the slope of the tangent at x=-1, then we can find slope of the normal and find the equation of it.
Differentiating the function w.r.t x, we get,
f'(x)=2(x-3)-2
We find the slope of the tangent at x=-1, we get
f'(-1)=-6
Slope of the tangent is -6, hence slope of the normal is 6 , this because the product of slope of tangent and slope of normal at a point is -1.
Before finding the equation, we need the value of f(x) at x=-1,
f(-1)=16
Now we have the point (-1, 16) and slope =6, which enough data to find the equation of the normal.
The equation of the normal is (y-16)=6(x+1)
On simplification, we get 6x-y+22=0

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