Question

Pre-AP *Pre*Calculus FRQ Help!

Answer 1

The table below shows function values and graphical properties for a cubic polynomial function, h(x), at indicated values or intervals of x.

Answer 2

x h(x)
(-inf,-3) Increasing & concave down
-3 3
(-3,-1) Decreasing & concave down
-1 1
(-1,1) Decreasing & concave up
1 -1
(1,inf) Increasing & concave up

Answer 3

a. At what x-values does the graph of h(x) reach a relative maximum? At what x-values does the graph of h(x) reach a relative minimum? Justify your answer.
b. Is either of the two relative extrema that you mentioned in part a an absolute extremum? Justify your answer.
c. At what x-value(s) does the graph of h(x) have a point of inflection? Justify your answer.
d. Sketch a possible graph of h(x).

Answer 4

hint for a:
if h is continuous at x=c
and the function h switches from increasing to decreasing at x=c
that is if we have something that looks like this:

then we have a max at x=c

but if the function h switches from decreasing to increasing at x=c
that is if we have something that looks like this:

then we have a min at x=c