Follow the steps below to estimate all of the solutions to the equation 3*sin(x)=12-5x.
a. Find a function f(x) such that the zeros of the function are the solutions to the equation.
b. Find an interval, one unit in length, on which you can use the IVT to show that the function f(x) has a zero on the interval. Be sure to clearly show that you have met the criteria necessary to use the theorem.
c. Now use Rolle's Theorem to show that it has exactly one zero. Be sure to clearly show that you have met the criteria necessary to use the theorem and explain how you are using the theorem to show t

Question

Follow the steps below to estimate all of the solutions to the equation 3*sin(x)=12-5x.
a. Find a function f(x) such that the zeros of the function are the solutions to the equation.
b. Find an interval, one unit in length, on which you can use the IVT to show that the function f(x) has a zero on the interval. Be sure to clearly show that you have met the criteria necessary to use the theorem.
c. Now use Rolle's Theorem to show that it has exactly one zero. Be sure to clearly show that you have met the criteria necessary to use the theorem and explain how you are using the theorem to show t

anonymous · Answer

hat the function cannot have more than one zero.
d. Use Newton's Method to approximate the zero to 4 decimal places. Show each approximation for the process.
e. Use Newton's Method to estimate the 4th root of 123 accurate up to 6 decimal places. Start with an integer initial approximation and show each iteration of the process.

anonymous · Answer

That's the problem in full, if someone could help I would really appreciate it, me and my friends are having trouble with it.

anonymous · Answer

The first part we're really having trouble on is part a, we have no idea how to start

anonymous · Answer

wow the rest is hard, part $a$ when i write it you will say "oh is that all?"

anonymous · Answer

$$3\sin(x)=12-5x\iff 3\sin(x)+5x-12=0$$ and so your function is 
$$f(x)=3\sin(x)+5x-12$$

anonymous · Answer

Is it really that easy?  The way they worded it made it seem way harder, especially the "zeros of the functions are the solutions to the equation"

anonymous · Answer

lol, yes, it is really that easy!

but it is what you want right?  you have methods to find the zeros of a function, so make sure to put everything on one side of the equal sign, that will give you the function that you want to find the zero of

anonymous · Answer

I'm pretty sure that's exactly what we're looking for, just the wording was throwing us all off for some reason.  We'll use that and try our best to figure out the rest.  Thanks!

anonymous · Answer

yw

anonymous · Answer

thanks for the help! I still can't figure out the last 3 parts. :(