MATH-UA 211 Study Guide - Final Guide: Piecewise, Square Root, Stationary Point

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cerisegiraffe538

17 Dec 2015

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Document Summary

Math-ua 211- lecture 1- functions of one-variable, domain/range, graphs, piecewise. X is the independent variable meaning it changes by itself. Y is the dependent variable meaning it depends on the change of x. A function (f(x)) is a formula that relates y to x and there are two criteria in order for a specific equation or graph to be a function. One value of x gives only one value of y. To figure out if a graph is a function or not, use a vertical line and check if there of multiple values of y for one x value. In order to make this equation a function, you must restrict the domain by getting rid of either the positive or negative part make it only one available value of y for each value of x. A domain is all x values for which the function is finite (ie. not infinity) Domain of y=x2+1 is all numbers except .

Related Questions

1. Local Versus Absolute Exterema. You might expect from single-variable calculus that if a function has one critical point and critical point is local minimum (say) then that critical point is the global/absolute minimum.

This fails spectacularly in higher dimensions (as there's a famous example of a mistake in a mathematical physics paper because this fact was not properly appreciated). you will compute a simple example in this problem.

Let

(a) Find all critical posints for this function in so doing you will se there is only one

(b) Verify this critical point is a local minimu.

(c) Show that is not absolute minimum be finding values of f(x,y) that are lower than the value at this critical point. We suggest looking at values f(0, y) for suitably chosen y.