Quartic Conjectures
Consider the function .
1. Find the tangent line to at the point . Can you do this in multiple ways?
2. Find a quadratic function whose graph is tangent to the graph of at the point .
3. Find a cubic function whose graph is tangent to the graph of at .
4. If dividing by gives a remainder whose curve is tangent to at , what do you think I must divide by in order to find a curve that is tangent to at the points AND at ? Find such a polynomial and graph it below.