Note: Make sure to use complete sentences when completing the following assignment.

Finding zeros of functions can be a very difficult task. Create two different methods for approximating a zero of a differentiable function.

  1. Create an algorithm to approximate a differentiable function that uses the intermediate value theorem;
  2. Create an algorithm to approximate a differentiable function that uses the concept of tangent lines.

Clearly state your algorithms and explain why you think they works. Use both algorithms to approximate a zero of the polynomial $p(x) = x^3+15.2x^2+.4$. Which one do you think is better and why.

Your solution should be no more than one page, front and back.