Precalculus · Problem 3.3.57

Polynomial Functions — Stitz & Zeager

Mathematics — Precalculus · polynomial-graph-analysis

Problem

Let

f(x) = 5x^7 - 33x^6 + 3x^5 - 71x^4 - 597x^3 + 2097x^2 - 1971x + 567

. With the help of your classmates, find the

x

- and

y

-intercepts of the graph of

f

. Find the intervals on which the function is increasing, the intervals on which it is decreasing and the local extrema. Sketch the graph of

f

, using more than one picture if necessary to show all of the important features of the graph.