Purchase Solution

Function, derivatives, error, and stationary points.

Not what you're looking for?

Ask Custom Question

See attached.

Consider the function of two real variables x and y (y not 1) defined by....
Find the first-order and second-order partial derivatives of f.
Determine the second-order Taylor polynomial for f near (0,-1)
Use first-order partial derivatives to determine the least and greatest possible values.
Use the chain rule to determine, in terms of t, the rate of change of f.
Locate and classify all the stationary points of f.

Attachments
Purchase this Solution
Solution Summary

This provides a series of problems involving a function, including partial derivatives, second-order Taylor polynomial, least and greatest possible values, maximum possible error, rate of change, and stationary points.

Solution Preview

(a) We have the following derivative calculations.

(b) From (a), we can get the second order Taylor polynomial for near the point . We have

(c) We only use the ...

Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • Four stationary points of a multivariable function

    , y1) = (0, 0) (x2, y2) = (-10, -10) (x3, y3) = (-4, 2) (x4, y4) = (2, -4) Stationary points are the points such that the partial derivatives of f(x,y) both with respect to x and y are 0.

  • Absolute minimum and maximum

    First find the interior stationary points by setting the partial derivatives to zero and solving simultaneously.

  • find out the stationary point, saddle point, min and max

    498301 find out the stationary point, saddle point, min and max 1) Let f(x,y)=25e^(-1/5x^2)-y^5+5y+3 a) Find all stationary points of the function f(x,y) and enter their coordinates by "" with at least 3 decimal places.

  • Stationary point

    For given function, stationary point is obtained. Followed by using first and second derivatives, left hand and right hand are classified. Finally y co-ordinate of the stationary point is obtained and the functions is drawn.

  • Derivatives / Chain Rule / Taylor Polynomials

    And finally how would I locate and classify all the stationary points of f?

  • Find Stationary Points and Inflexions of a cubic polynomial

    (a) Find the condition on the constants a,b,c so that this function has two stationary points. (b) Find the x-values of the stationary points (and do not try to find the y-values).

  • Finding extreme values for functions of two variables

    This approach can be generalized to functions of two variables, where finding stationary points involves simultaneously solving for stationary points of the partial derivatives and then applying a more generalized "second derivative" test to describe

  • Derivatives and Maximum Profit

    (c) Calculate Dv/dr and d2V/dr2 (d) Find the stationary points of V and determine their nature. Hence state the maximum volume of the cylinder (correct to 2 decimal places). (e) Sketch the graph of V as a function of r.

  • An open-top box is to be made as follows...

    Use derivatives to identify all local maxima and/or minima of f, if any. The maxima or minima happens when The stationary points are . is a singular point, at which f(x) is undefined. So we won't consider this point.

View More Related Solutions