Let p(x)=−x4+4x2. Study its behaviour on the interval [−3,3].
a. (a) Using a step length of 0.5 in x, complete a table of values of p(x) for x=−3,−2.5,−2,…,3.
b. (b) Plot these points accurately on graph paper and join them smoothly to obtain the curve of y=p(x).
c. (c) From your sketch, describe the orientation of the "arms" of the curve and explain briefly how the sign of the leading coefficient influences this orientation.
d. (d) Using the graph, estimate the range of p(x) on [−3,3].