What is the equation of the line normal

George Michael

George Michael

Answered question

2022-04-09

What is the equation of the line normal to f(x)=4x27x+6 at x=1?

Answer & Explanation

Emily Green

Emily Green

Beginner2022-04-10Added 14 answers

At x=1, f(x)=4-7+6=3, hence normal will be at point (1,3) on the curve
f(x)=4x27x+6.
The slope of tangent will be given by value of f'(x) at x=1
As f'(x)=8x-7, slope of tangent is 1.
As normal is perpendicular to tangent, slope of normal will be 11=1;
Hence equation of normal given by point slope form will be
(y-3)=-1*(x-1) or y-3=-x+1 or x+y=4

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