Follow the steps below to estimate all of the solutions to the equation 3sin(x)=12-5x.
a)find an interval, one unit in length, on which you can use the Intermediate Value Theorem to show that the function f(x) has a zero on the internal. Be sure to clearly show that you have met the criteria necessary to use the theorem.
b) 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.

Question

Follow the steps below to estimate all of the solutions to the equation 3sin(x)=12-5x.
a)find an interval, one unit in length, on which you can use the Intermediate Value Theorem to show that the function f(x) has a zero on the internal. Be sure to clearly show that you have met the criteria necessary to use the theorem.
b) 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.

anonymous · Answer

x = 1.8182810062556485 to 16 digits.
Refer to the attachment from Mathematica.