Question

Consider the function g defined by g(x) = x(10 – Ax), A > 0. voer g in Without doing any iterations, determine the non-zero fixed point(s) of g in terms 7 of A.

Answer 1

Answer:

The only non-zero fixed point is:  x = 9/A.

The Step-by-step explanation:

A fixed point of a function is a points that is mapped to itself by the function; g(x) = x. Therefore, in order to find the fixed point of the given function we need to solve the following equation:

g(x) = x

x(10 - Ax) = x

10x - Ax² = x

10x - x -Ax² = 0

9x - Ax² = 0

Ax² - 9x = 0

The solutions of this second order equation are:

x = 0 and x = 9/A.

Since we are only asked for the non-zero fixed points, the solution is: 9/A.