Find the equation of the osculating circle at the local minimum of f(x) = 3x + lx² + -80 x+7 %3D

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Find the equation of the osculating circle at the local minimum of
f(x) = 3x + 1æ² +
-80
x+7
9.
Transcribed Image Text:Find the equation of the osculating circle at the local minimum of f(x) = 3x + 1æ² + -80 x+7 9.
Expert Solution
Step 1

Given equation ,

fx=3x3+1x2+-809x+7

f'x=9x2+2x+-809

For critical point f'x=0

9x2+2x+-809=081x2+18x-80=0

by solving the quadratic equation we get,

x1=-1.111x2=0.888

f''x=18x+2f''-1.111=18×-1.111+2=-17.98<0

So this is the point of local minimum

 

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