Drawing the Graph of a Function

• Sketching the graph of a polynomial function
  1. $\rhd$ Curve sketching with calculus: polynomial (20:30) Sketch the graph of $f(x) = 3x^4 -4x^3+2$ using derivatives.
  2. $\rhd$ Analyzing a function with its derivative (9:41) Sketch the graph of $f(x)=x^3-12x-2$ using derivatives.

• Sketching the graph of a rational function
  1.  Curve sketching with calculus: rational function

Graph $y=\dfrac{x-1}{x^2}$.

1. 1. 1. $\rhd$ Part I (10:00): Find the domain, intercepts, symmetry relations, asymptotes, intervals of increase/decrease, and local extrema.
      2. $\rhd$ Part II (8:04): Find the intervals of concavity and skech the graph of the function.