Question 356044
I used Newton's method in an EXCEL spreadsheet with a starting value of {{{x1=0.5}}}.
f(x)={{{sin(x)+cos(x)-6x}}}
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{{{graph(300,300,-5,5,-5,5,sin(x)+cos(x)-6x)}}}
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f'(x)={{{cos(x)-sin(x)-6}}}
x(n+1)=x(n)-f(x(n))/f'(x(n))
The solution quickly settled to {{{x=0.195923}}}