Question

Use Newton’s Method to approximate a **critical
number** of the function ?(?)=(1/3)?^3−2?+6.
f(x)=1/3x^3−2x+6 near the point ?=1x=1. Find the next two
approximations, ?2 and ?3 using ?1=1. x1=1 as the initial
approximation.

Answer #1

given f(x)=(1_{/3})x^{3}-2x+6

=>f '(x)=(1_{/3})(3)x^{3-1}-2(1)+0

=>f '(x)=x^{2}-2

for critical points f '(x)=0

=>x^{2}-2=0

let p(x)=x^{2}-2

=>p'(x)=2x^{2-1}-0

=>p'(x)=2x

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