Concept explainers
Analyzing critical points Find the critical points of the following functions. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a
30.
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
Precalculus
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
- 1. Given the function f(x) =(x-2)^2 +(y-3)^2 (i) Find the critical points. (ii) Using the second derivative test, Classify the critical points .arrow_forwardHi. If by second derivative test, if x = a is a critical point of f(x) and f''(a) > 0, then (a, f(a)) is a point of local minimum. Can you explain why my answer is wrong?Thank you so much!arrow_forwardDetermine the critical point of the function and use the critical studied to classify it(s) as a maximum, minimum or saddle point. Z=e^xyarrow_forward
- Find the critical point of the function f(x,y)=6x−2y^2−ln(|x+y|). c=Use the Second Derivative Test to determine whether it isA. a saddle pointB. a local maximumC. test failsD. a local minimumarrow_forwardFind the critical point of the function f(x, y) =-(8x+2y2 +ln(|x+y|)).c = Use the Second Derivative Test to determine whether it is• A. a local maximum• B. a saddle point• C. a local minimum• D. test failsarrow_forwardFind the x-coordinates of all critical points of the given function. Determine whether each critical point is a relative maximum, a relative minimum, or neither, by first applying the second derivative test, and, if the test fails, by some other method. g(x) = 2x3 − 24x + 8 Step 1 Recall that a critical point is any interior point x in the domain of f where f '(x) = 0 or f '(x) is not defined. To find the critical points of g(x), first find the first derivative g'(x). Since g(x) = 2x3 − 24x + 8, then g'(x) = x2 − 24.arrow_forward
- a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and minimum values.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist). ƒ(x) = √x ln x on (0, ∞)arrow_forwarda. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and minimum values.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist).arrow_forwardI'm currently learning how to find critical points and to determine the local max and minimum. I also learned to determine when the function is increasing and decreasing using intervals, but I'm having a hard time to find the first & second derivative for the function below. I want to make sure I'm in the right path for both the 1st and 2nd deriv. I will try to find the local max and minimum on my own. Ty. y = x^5/3 - 5(x)^2/3arrow_forward
- Use the level curves in the figure to predict the location of the critical points of f and whether f has a saddle point or a local maximum or minimum at each critical point . Explain your reasoning. Then use the Second Derivative Test to confirm your predictions . 3.f(x,y)=4+x3+y3-3xyarrow_forward(a) For the following functions, (1) find the critical values and (2) determine if at these points the function is at a relative maximum, relative minimum, inflection point, or saddle point. (I) f (x, y) = 60 + (x-y)3 + (y-1)3 (II) f (x, y) = 2 + x2 + y2arrow_forwardFind the critical points of the following function. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the critical points. f(x,y) = sqrt(x2+y2+2x2+10)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage