Showing that four stationary points of a multivariable function are at specific points.

A surface is described by the multivariable function f(x,y) where: f(x,y) = x^3 + y^3 + 9(x^2 + y^2) + 12xy a) Show that the four stationary points of this function are located at: (x1, y1) = (0, 0) (x2, y2) = (-10, -10) (x3, y3) = (-4, 2) (x4, y4) = (2, -4)

Real analysis

We are learning Rolle, Lagrange, Fermat, Taylor Theorems in our Real Analysis class. We just finished continuity and are now studying differentiation. We are using the books by Rudin, Ross, Morrey/Protter. ****************************************************** Let f: [a,b] --> R, a < b, twice differentiable with the second der ...continues

Real analysis

Based on the Rolle, Lagrange, Fermat and Taylor Theorems. ****************************************************** Let f: [a,b] --> R, a < b, twice differentiable with the second derivative continuous such that f(a)=f(b)=0. Denote M = sup |f "(x)| where x is in [a,b] and g:[a,b] --> R, g(x)=(1/2)(x-a)(b-x) i) Prove ...continues

Real Analysis Problem

We are learning Rolle, Lagrange, Fermat, Taylor Theorems in our Real Analysis class. We just finished continuity and are now studying differentiation. We are using the books by Rudin, Ross, Morrey/Protter. ****************************************************** Let f: [a,b] --> R, a < b, twice differentiable with the second d ...continues

Real Analysis Problem

We have learned Rolle, Lagrange, Fermat, Taylor Theorems in our Real Analysis class and we have finished differentiation. We just started integration. In this problem we are not supposed to use any material we haven't learned, ie integration. We are using the books by Rudin, Ross, Morrey/Protter. **************************** ...continues

Real Analysis Problem

We have just finished up integration and are done with a first course in analysis, chapters 1-6 of Rudin. We are also using the Ross and Morrey/Protter book. Please answer question fully and clearly explaining every step. Any solution short of perfect is useless to me. So if you are not 100% sure whether your answer is right, ...continues

Real Analysis Problem

We have just finished up integration and are done with a first course in analysis, so chapters 1-6 of Rudin. We are also using the Ross and Morrey/Protter book. Please answer question fully and clearly explaining every step. Any solution short of perfect is useless to me. So if you are not 100% sure whether your answer is right, ...continues

Real Analysis Problem

I need a correct and concise solution. The Problem: f : R --> R , f ' ' ' ' continous. Prove: S (from a to b) f (t) dt = [(b - a) / 6] ( f(a) + f(b) + 4 f( (a+b) / 2) ) for all a, b in R. f ' ' ' ' means four times differentiable. S means the integral

Real Analysis Problem

I need a correct and concise solution. If the answer is not 100% correct, I will ask for my money back! We just finished integration and are done with a first course in analysis, i.e. chapters 1-6 of Rudin. We are also using the Ross and the Morrey/Protter book. The Problem: f : R --> R , f ' ' ' ' continous. ...continues

Completing the square: Finding the vertex and intercepts - repel, attract or are indifferent?

Rewrite the function f(x)=x^2+13/3 x+7/3 in the form f(x)=(x+13/6)^2+ c Then need to find the vertex of parabola as the graph of f, finding the y and x intercepts. Find the fixed points of f state whether they repel, attract or are indifferent. Using a gradient, find the interval of attraction for one of the fixed ...continues