After a presidential election, the proportion h(p) of seats in the House of Representatives won by the party of the winning presidential candidate may be modeled by the cube rule

where p is the proportion of the popular vote received by the winning presidential candidate.

a. Find h'(p) and h"(p).

b. Sketch the graph of h(p).

c. In 1964, the Democrat Lyndon Johnson received 61% of the popular vote. What percentage of seats in the House does the cube rule predict should have gone to Democrats? 

Transcribed Image Text:

h(p) p p³ + (1 − p)³ 3 - for 0 ≤p ≤ 1