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

In class we talked about how the intermediate value theorem could be used to create an algorithm to approximate a root of a function. Use the concept of the tangent line to create a new algorithm for finding zeros of differentiable functions. Clearly state your algorithm and explain why you think it works. Use your algorithm to approximate a zero of the polynomial $p(x) = x^3+15.2x^2+.4$.