Mathematics

Problem

84. Looking Ahead to Calculus Consider the function

f(x)=x^{n}

where

n

is an odd integer. (a) Suppose that

a

is a positive number. Show that the slope of the line through the points

P(a, f(a))

and

Q(-a, f(-a))

a^{n-1}

. (b) Let

x_{0}=a^{1 /(n-1)}

. Find an equation of the line through point

\left(x_{0}, f\left(x_{0}\right)\right)

with the slope

a^{n-1}

. (c) Consider the special case

n=3

and

a=3

. Show both the graph of

f

and the line from part b in the window

[-5,5]

[-30,30]