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 that 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.

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 that 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.