What is the equation of the normal line

Emmy Decker

Emmy Decker

Answered question

2022-04-09

What is the equation of the normal line of f(x)=x4+4x3x2+5x6 at x=2?

Answer & Explanation

libertydragonrbha

libertydragonrbha

Beginner2022-04-10Added 15 answers

As the function is f(x)=x4+4x3x2+5x6, the slope of tangent at any point will be the value of f'(x) at that point.
As f(x)=4x3+12x22x+5, the slope of the tangent at x=2 will be
423+122222+5=32+484+5=17.
And slope of normal would be 117=117
Note that value of function at x=2 is f(x)=24+42322+526
=16+32-4+10-6=48
Hence, slope of normal is 117 and it passes through (2, 48)
its equation of normal is y48=117(x2) or 17(y-48)=-x+2 or
x+17y-818=0

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