arrggh! newton-raphson nightmare, textbook mistakes?!?!

the equation in question is 3sin(x+3)=cos(2x) to 4 dp between 0 =< x =< 7

by rearranging the equation i get f(x) = 3sin(x+3)-cos(2x) which im sure is correct as this is what i get in maple and calculus bagatirx

next step is to check by basically guess

so I guess 3.5 which is -0.10854 and 3.75 is 1.0034 so i think ok jackpot I'm close enough

anyway I differentiate it to 3COS(x+3) + 2sin(2x)

I then calculator using general iteration formula which is xnew= x(-0.10854) - f(x)/f'(x)

I run this continually until i get -0.1765 and this is what the newton-raphson calculator online confirms it as

my book states the answer is 3.524 and 6.1067 I MEAN WTF IS THAT??!! is my answer wrong, am I doing something wrong?

or is my book full of **** (which it has been lately, alot of stuff is incorrect but I can't rule it out that I haven't made a mistake or whether the fact the book is wrong)

Reply 1

aznkid66

I think there's a root at -0.1765, although that root isn't in the domain 0 ≤ x ≤ 7. I got 6.1067, but not 3.524. I don't understand how you can have two values, so I too am confused by your textbook. o.o