AP Precalculus / Unit 1: Polynomial and Rational Functions
1.4 Polynomial Functions and Rates of Change
Notes
A polynomial $p(x)=a_nx^n+\dots+a_0$ has degree $n$ (highest power).
- Local max/min: where the graph changes from increasing to decreasing or the reverse.
- Point of inflection: where concavity changes.
- A degree-$n$ polynomial has at most $n-1$ turning points.
Practice
The maximum number of turning points for a degree-5 polynomial:
At most $n-1$.
Where the graph switches from increasing to decreasing, there is a:
A peak.
Where a graph changes from concave down to concave up, there is:
Concavity switches.
Ready for more? Take the Unit 1 test.