6. Consider the function f(x)= 2x° –6x² – 18x+22. Use the Second Derivative Test to find the relativeextrema, if any, of the function. (Give your answers as ordered pairs.)f' (2) = 6x2 - 12x -18f'(2): 0( 3x +3)(2x-6) - o3x +3 =0dx -6-0I= -13fr (x) = 12x -12f" (-) = -12- 12= -24rmaxat x= - 241"(3)36 - 1224 sSorminat gH= 24=ニt(- 24) = 2(-24)3 -6( -24)2 -18(-24) + 22 = - 27338f (24) = = 270942C 24)% - 6C 24)² - 18 (24)+ 22(-24, -Relative minimum(s): 24, 27094)27338)Relative maximum(s):

Answered: Image /qna-images/answer/55c4bde8-eeed-432b-b2f8-d44e717a142c.jpg

Answered: 6. Consider the function f(x)= 2x3 -…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

What is the value of the first order derivative of the closed function given as x3+y3+3xy+3y2+6x+6y=0 at the point x = 1 ?
4- Calculate the second derivative of the function y = f (x) defined by the equationx3 + y3 +3xy + 3y2 + 6x + 6y =0 at the point x = 1
The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos (8x+6) 4. y' = 24 cos (8x+6)
• Show that both of the functions f(x) = (x − 1)^4and g(x) = x^3 −3x^2 + 3x+ 2 have stationary points at x = 1.• What does the second derivative test tell you about the nature of these stationary points?• What does the first derivative test tell you about the nature of these stationary points?
Approximate the derivative of the function f(x) = 2x^3 - 5x^2 + 3x - 1 at x = 2 using the forward difference formula with a step size of h = 0.1.
The derivative of y = sin(e2x) is: 1. e2xcos(e2x) 2. 2cos(e2x) 3. 2e2xcos(e2x) 4. 2xcos(e2x)
C(0) = 1000 and C'(x) = 400e^(-0.1q) + 8. Then C(x) is A. -4000e^(-0.1q) + 8q + 1000 B. -4000e^(-0.1q) + 8q + 5000 Notice that both A and B satisfy the 2nd condition: derivative of A or B = -4000e^(-0.1q)(-0.1) + 8 + 0 = 400e^(-0.1q) + 8. But which one satisfies the 1st condition also?
2. Find the equation of the line that is tangent to the curve y3 + 3y = x2 at the point (2, 1).

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

6. Consider the function f(x)= 2x3 - 6x2 – 18x+22. Use the Second Derivative Test to find the relative extrema, if any, of the function. (Give your answers as ordered pairs.) f' (2) = 6x2 - 12x -18 f'(x)=0