1. Let [math]f\left(x\right)=5x^3+4x-7[/math]. (This is the same cubic from Chapter 1.) Find a constant, linear, and quadratic Taylor polynomial for [math]f\left(x\right)[/math] centered at [math]x=3[/math].
2. Graph your constant, linear and quadratic Taylor polynomials and [math]f\left(x\right)[/math] on the set of axes below.
3. What do you notice? What can you say about these Taylor polynomials near the point [math]\left(3,f\left(3\right)\right)[/math]?