What is the equation of the line normal

Eddie Clarke

Eddie Clarke

Answered question

2022-04-10

What is the equation of the line normal to f(x)=x36x at x=2?

Answer & Explanation

Zaria Lamb

Zaria Lamb

Beginner2022-04-11Added 8 answers

Explanation:
the given: f(x)=x36x at x=2
Find the value of the function at x=2
f(2)=(2)36(2)=812=4
f(2)=-4
The point on the curve is (2, -4)
Find first derivative f'(x) then evaluate at x=2
f(x)=3x26
f(2)=3(2)26
m=6 to be used for Tangent line.
m(perpendicular)=16 to be used for the Normal Line
Use now the m=16 and the point (2, -4)
The Normal Line:
yy1=m(xx1)
y(4)=(16)(x2)
y+4=(16)(x2)
6y+24=-x+2
6y=-x-22
y=x6113 the required Normal Line

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