MATH 1XX3 Lecture Notes - Lecture 32: Fxx, Saddle Point

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2 Apr 2016

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" f " lx ) is used to find maxslmins. Terminology : f ( x , y fcx. ) has a local max at (a , b) ( a , b) local min at. If (a , b) flx , y ) for all ( x . y ) ( x , g) for all ( x , g) If fy (a , f has a local maxlmin at (a , b) and if fx and fy are defined. , then fx (a , b) and: = 0. Consequence : at local maxlmin of ( a , b) a. Geometrically : you cannot move in any direction and increase decrease your height. Definition : the critical points of flx , y ) are all the points (a , b) such that fx (a . b) =o fylabl o fx. , fy or do not exist at ( a , b) " 2 } only one critical point p= (-2 ,

Related Questions

Consider the function f(x,y)= x^4+y^4-4 xy+2. on D = [-3,3]x[-3,3] a. Find the absolute and relative maxim a and minima if they exist. Proceed as follow b. Compute the first-order partial derivatives c. Find the critical points d. Compute the second-order partial derivatives e. Use the second derivatives test to classify the critical points f. Find the value of the function at the local extrema if they exist g. Find the absolute maxima and minimum by evaluation f on the boundary of D

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If U and V are positive constants, find all critical points of the function. (Enter your answers as a comma-separated list.) F(t) = Ue t + Ve -t t = Find all critical points of f(x) = 20 x 2 e - 0.3x and classify them as local minima of ,maxima. x = (smaller value) This critical point is a . x = (larger value) This critical point is a . Consider f(x) = x 8 (7 - x) 9. Find f '(x) and simplify your answer. f '(x) = Find all critical points of f(x) and then use the first derivation test to determine local maxima and minima. f(x) has a at x = (smallest value) Local Maximum OR Minimum OR Neither f(x) has a at x = Local Maximum OR Minimum OR Neither f(x) has a at x = (largest value) Local Maximum OR Minimum OR Neither Find the inflection points of f(t) = t 4 + t 3 - 18t 2 +8. Give exact answer. t = (smallest value) t = (largest value) Sketch a possible of y = f(x), using the given information about derivation y' = f'(x) and y" = f"(x). Assume that the function is defined and continuous for all real x. Let f be a function f(x) > 0 for all x. Let g = 1/f. If f is increasing in an interval around x 0, what about g? g is increasing in an interval x 0. g is zero in an interval around x 0. g is decreasing in an interval around x 0. We cannot tell whether g is increasing or decreasing in an interval around x 0. g is constant in an interval around x 0. If f has a local maximum at x 1, what about g? g has a local maximum at x 1. g has both a local minimum and a local maximum at x 1. We cannot tell whether g has a local minimum or a local maximum at x 1. g has an inflection point at x 1. g has a local minimum at x 1. If f is a concave down at x 2, what about g? g is increasing at x 2. g is flat at x 2. We cannot tell whether g is concave up of concave down at x 2. g is concave down at x 2. g is concave up at x 2. You are given the graph of the second derivation function f" below. Which of the given have x-values that are inflection points of the function f? (Select all the apply.) A B C D E F G H I none of the above

MATH 1XX3 Lecture Notes - Lecture 32: Fxx, Saddle Point

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