What is the equation of the line that

Breanna Mcclure

Breanna Mcclure

Answered question

2022-04-08

What is the equation of the line that is normal to f(x)=2x33x2+5 at x=1?

Answer & Explanation

madking711kzcb

madking711kzcb

Beginner2022-04-09Added 9 answers

The normal line is the vertical line through the point (1,4). Its equation is x=1
Explanation:
At x=1, we have y=4, so the line we want contains the point (1,4)
The tangent at that point has slope f'(1).
Since f(x)=6x26x, we get a slope of 0.
The tangent line is horizontal. The normal line is perpendicular to the tangent line, so the normal line is vertical.

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