Using original assumption combined w MVT (f(b)-f(a))/(b-a)
Define point of inflection from δ
For x_0 €R , δ>0
6 steps of graph sketching
1) natural domain
2) asymptotes
3) find discontinuities and their types
4) find zero and intervals of constant sign
5) extrema and intervals of monotonicity
6) intervals of convexity/Concavity