Mathematics

Problem

Two quadratic-type curves

y=x^2

and

y=x^4

are to be compared on the same set of axes. a. (i) Show algebraically that for all real

x

with

|x|<1

x^4 < x^2

, and for all real

x

with

|x|>1

x^4 > x^2

. b. (ii) Using part (i), explain which curve lies closer to the

x

-axis near the origin and which one grows more rapidly for large

|x|

. c. (iii) Sketch both curves on the same set of axes, clearly indicating the regions identified in part (ii).