Analyzing critical points Identify the critical points of the following functions. Then determine whether each critical point corresponds to a local maximum , local minimum , or saddle point. State when your analysis is inconclusive. Confirm your results using a graphing utility. 87. f ( x , y ) = 10 – x 3 – y 3 – 3 x 2 + 3 y 2
Analyzing critical points Identify the critical points of the following functions. Then determine whether each critical point corresponds to a local maximum , local minimum , or saddle point. State when your analysis is inconclusive. Confirm your results using a graphing utility. 87. f ( x , y ) = 10 – x 3 – y 3 – 3 x 2 + 3 y 2
Analyzing critical pointsIdentify the critical points of the following functions. Then determine whether each critical point corresponds to a local maximum, local minimum, or saddle point. State when your analysis is inconclusive. Confirm your results using a graphing utility.
87. f(x, y) = 10 – x3 – y3 – 3x2 + 3y2
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
Determine the critical point of the function and use the critical studied to classify it(s) as a maximum, minimum or saddle point.
f(x,y)=-5x²+4xy-y²+16x+10
(a) Approximately, find the x-coordinates of the critical points of g(x).(b) Approximately, find the absolute minimum and the absolute maximum values of the function g(x). Express your answer as (x, y) .
(c) Approximately, find the inflection points of g(x). Express your answer as (x, y).
Q3: Find the critical points of the following function then test them for local maximum, local minimum and saddle point. f (x, y) = x3 + y3 - 3xy + 15
Chapter 15 Solutions
Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.