What is the equation of the normal line

Papierskiix5n

Papierskiix5n

Answered question

2022-04-09

What is the equation of the normal line of f(x)=7x3x2x1 at x=-8?

Answer & Explanation

Kendall Wilkinson

Kendall Wilkinson

Beginner2022-04-10Added 17 answers

f(8)=7(8)3(8)2(8)1=3527.
f(x)=21x22x1.
f(8)=21(8)22(8)1=1329
Hence the slope of the tangent at x=-8 is -1329.
But the normal is perpendicular to the tangent and hence the slope of the normal at that point is m=11329
But the normal line is a straight line so of form y=mx+c.
Substituting the point (x,y)=(-8, 3527), we get for the normal :
3527=11329(8)+c
c=3527
Thus the normal has equation y=11329x+3527

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