1. Find the tangent line to [math]f\left(x\right)[/math] at the point [math]x=-1[/math]. Can you do this in multiple ways?

2. Find a quadratic function whose graph is tangent to the graph of [math]f\left(x\right)[/math] at the point [math]x=-1[/math].

3. Find a cubic function whose graph is tangent to the graph of [math]f\left(x\right)[/math] at [math]x=-1[/math].

4. If dividing [math]f\left(x\right)[/math] by [math]\left(x+1\right)^2[/math] gives a remainder whose curve is tangent to [math]f\left(x\right)[/math] at [math]x=-1[/math], what do you think I must divide [math]f\left(x\right)[/math] by in order to find a curve that is tangent to [math]f\left(x\right)[/math] at the points [math]x=-1[/math] AND at [math]x=3[/math]? Find such a polynomial and graph it below.