Answered: critical values of ?(?) = 4?3 − 48? +…

critical values of ?(?) = 4?3 − 48? + 24 are x = -2 and x = 2. Determine which of the critical values correspond to a local minimum. x = 2 x = -2 x = 2 and x = -2 neither x = 2 nor x = -

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 3SE: How are the absolute maximum and minimum similar to and different from the local extrema?

See similar textbooks

Related questions

Q: Find the critical numbers of the function

A: We find g'(y) using the quotient rule

Q: A function f(x) has a critical number x=c. Which of the following statements is always true about…

Q: 3. Let f(r, y)- e (a) Verify that (0, 0) is a critical point. (b) Is this critical point a local…

Q: Find the minimum and maximum value of the function on the given interval by comparing values at the…

A: We have given a function y = x3 - 12x2 + 21x To find: The mnimum and maximum value of the function…

Q: Minimize ?=?+3?+10 subject to: 2?+4?≥8 4?+3?≥12 ?,?≥0 Corner points at…

A: The objective function is given as, Zx,y=x+3y+10 Subjected to the following constraints,…

Q: The function k(x, y) = e cos(4x) has a critical point at (0, 0). What is the value of D at this…

Q: 3. The Critical Point of y=xe*

Q: Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated condition.…

Q: a. I b. | function f(x, y) = y² − x² + - the critical points of the function f(x, y) = y² − x² + -…

Q: fc is a critical point of F(x), when the is a local maximum or minimum at c? Explain

Q: Obtain the particular solution satisfying the initial conditions indicated.

Q: 1. Given that f ( x , y ) = xy² - y? - 2x? + 10 , find the critical points and determine the…

Q: The curve ax4+bx3+cx2+dx+k passes thru P1 (5, –210), has a critical point at P2 (4, –416), and an…

A: Given The curve ax4+bx3+cx2+dx+k passes through P15,-210, has a critical point at P24,-416 and an…

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 2x?.…

A: The given function is f(x, y) = 2x2 - 5x - 3y + 5y2 To find the critical points of the function.

Q: The function f(x, y) = 2x² + y² – 3xy – 2x + y – 2 has one critical point. Find it, and determine if…

A: take the partial derivative with respect to x

Q: find the minimum and maximum value of the function on. the given interval by comparing values at the…

Q: critical point of y = xe*

A: Given: y=xex We know that for any given functiony=fx in it's domain, at critical point either…

Q: Find and identify all critical points for the function f(x, y) = 4:r³ + 2ry? + 1022 + 2y? as a local…

Q: Let f(x) = x? (6 – x)3 (a) Find all critical point of f(x). (b) Classify each critical point as a…

Q: Designer functions Design a sine function with the givenproperties.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: nsider the autonomous ulmerentiai equation y' = y(2 – y)(4 – y) nd the DISTINCT critical points and…

A: Given differential equation is y'=y2−y4−y

Q: Calculate all of the critical points of the function: 2 f(x, y) = x² + y² + xY is a relative minimum…

A: To find the relative maxima and minima of the given function.

Q: For what values of the constant k does the Second Derivative Test guarantee that ƒ(x, y) = x2 + kxy…

A: Consider the equation

Q: What is the long term behavior of the solution with the initial condition (-2, 2)? 3 1 -1 5A4 -2 514…

A: Find your answer below

Q: (a) Show that there are two possible equilibrium values for p in [0,1] (which you should calculate)…

A: We have, dpdt=cp1-p-p2 For the equilibrium point we have, dpdt=0cp1-p-p2=0pc1-p-p=0p=0or…

Q: For the functions f(x,y) = 3 × y – x³ - y³ , which options are correct (there are more than one…

A: According to the given information, it is required to find the correct options for the given…

Q: Find the minimum and maximum value of the function on the given interval by comparing values at the…

A: To find: The minimum and maximum value of the function on the given interval by comparing values at…

Q: Classify the critical point (0, 0) as to type, and determine whether it is stable, asymptotically…

Q: The function f(x) = x^3 + bx^2 + c has a critical point at (-2, 6). Determine the value of b and c.

Q: The curve y = ax³ + bx² + cx + d has a critical point at (-1,3) and has a point of inflection at…

A: We are asked to which is true for the given condition Note: Critical points are points where the…

Q: The function k(x, y) = e cos(2x) has a critical point at (0,0). What is the value of D at this…

Q: (a) False. For example, x = 0 is a critical point off (x) = x 3 but is neither a local minimum nor a…

A: Given:fx=x3 , x=0 is a critical point

Q: Find the critical points of y= 2x^3 +3x^2–12x and apply the Second Derivative Test to find the…

Q: Classify the critical point (0, 0) as to type, and determine whether it is stable, asymptotically…

Q: For the following functions, (1) find the critical values and (2) determine if at these points the…

Q: 5. Find the critical point and determine whether local maximum or minimum: y = e" + e-2aæ

Q: Find the critical numbers of the function. y - 3 y2 – y + 3 g(y) = y = 0 (smaller value) y = 3 |×…

Q: Let f (x, y) = (4xy – 2)3 + e2x, then find: f.ry(1,–1)

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: What is the best description of point (0, 0) on the plot C) above? (i) Local minimum (ii) Local…

A: At point (0,0) As we move in +ve x -direction, from x = (-2,2) and keeping y = 0.For x(-2,0) :…

Q: Assume that ?(?)=x3+bx2+cx where b and c are constant coefficients. Find the values of b and c such…

A: For critical points :-f'(x)=03x2+2bx+c=0Given that critical point is at x=1So,3+2b+c=0 ..(1)

Q: (a) Find the general solution of the equation (x – 2) y dr 3(х — 1) -y3 1 - (x + 1) (b) Given the…

A: A first-order linear ordinary differential equation(ODE) is of the form y'(x)+p(x)y=q(x). The…

Q: 1) A rectangular steel sheet is bounded by the axis x = 0, y = 0, x = a and y = b. The temperature…

A: We solve this by following method

Q: f(x,y) = (x² + y²)e»²-

Q: 6. Find all critical points of f(x, y) = 2y* + x² – 6xy and classify each critical point as a local…

Q: Each of the following functions has at most one critical point. Graph a few level curves and a few…

A: Consider the given using graphing calculator: let fx, y=e-x2-y2

Q: 3. The Critical Point of y = xe-*

Q: Use Improved Euler's Method to approximate a solution y(x) to the problem of initial value [image]…

A: Given differential equation with initial value is y'=1+(x-y)2 , y(2)=1 Let f(x,y)=1+(x-y)2 We have…

Q: Classify the critical point (0, 0) as to type, and determine whether it is stable, asymptotically…

Question

The critical values of ?(?) = 4?³ − 48? + 24 are x = -2 and x = 2. Determine which of the critical values correspond to a local minimum.

x = 2
x = -2
x = 2 and x = -2
neither x = 2 nor x = -

Formula Formula A function f ( x ) is also said to have attained a local minimum 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 a case f ( a ) is called the local minimum value of f ( x ) at x = a .

Expert Solution