A number (a) is called a fixed point of a function (f) if f(a)=a. Prove that, if f'(x) does NOT equal 1 for all real numbers (x), then f has at most one fixed point.

Solution Summary

The mean value theorem is used to provide a proof regarding fixed points. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

... (ii) Starting with X0 = 8.4, use this fixed point iteration to ... 0.5794>0, f(0.7)=-0.2300<0, f(8.3)=-0.0488<0, f(8.5)=0.0798>0 By the mean value theorem, f ...

... is for the whole population, and as such, it is a fixed value. ... standard deviation of the distribution of the sample mean over repeated ... (a) A point estimate is ...

... integrable in the sense of Riemann" and the value of the ... the definite integral can be computed by means of the ... function y = f ( x) (1) and a fixed point (A) on ...

... is to serve as a "best guess" for an unknown (fixed or random ... is useful to give more weighting to certain data points, in which ...Mean = Total / number of items. ...

... passing through a point x0 > 0 reaches a fixed point in ... we see that all trajectories pass through the point x ( x0 2 ... x0 2/3 ) = ( 0, 0 ) , ie, the origin of the ...

... As above, the conflict theorist would point out that ... will radically change his/her self-definition in prison ... The self-concept is not fixed and unchanging if ...

... test is to be decreased, then for a fixed sample size n. ... Table 10-5, the value of the sample mean difference is ... Question 8 4 points Save In what type of test is ...

... per unit through increased production since fixed costs are ... So it was considered that the minimum point of the ... the practice of the monopolist to fix the price ...

... part (b). (That is the function f has a unique fixed point.). ... such that g(a) > g(x), and a point y belonging ... f (x) is continuous at x = 0. This means that for ...

... issues in order to find ways to fix them. ... of friction in order to ascertain remedies in fixing parent and ... culture, values, they are seen as points of reference ...