Sketch a possible graph of a function of that satisfies the following conditions.(1)f'(x) > 0 on (-∞0, 3), f'(x) < 0 on (3, 00)F"(x) > 0 on (-∞, -6) and (6, co), F"(x) < 0 on (-6, 6)lim f(x) = -3, lim f(x) = 0SolutionCondition (i) tells us that f is increasing on (-00, 3) and decreasing on (3,00). Condition (ii) says that f is concave upward on -00,First we draw the horizontal asymptote y = -3 as a dashed line (see the figure).yAr36,00)..and concave downward onFrom condition (iii) we know that the graph of f has two horizontal asymptotes: y =ⓇWe then draw the graph of f approaching this asymptote at the far left, increasing to its maximum point at x = 3 and decreasing toward the x-axis at the far right. We also make sure that the graph has inflection points when x = -6 andis betweenand 6.and y = 0.. Notice that we made the curve bend upward for x < -6 and x > 6, and bend downward when x

We have to fill in the blanks from the given information.

Answered: Sketch a possible graph of a function…

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

Sketch a possible graph of a function that satisfies all of the following conditions: f'(2) = 0, f'(0) =1, f'(x) > 0 if 0 2, f"(x) 0 if x > 4, lim, 00 f(x) = 0, and f(-x) = -f(x) for all x.
Let P = (x, y) be a point on the graph of y = x2 - 8.(a) Express the distance d from P to the point (0, - 1) as a function of x.(b) What is d if x = 0?(c) What is d if x = - 1?(d) Use a graphing utility to graph d = d(x).(e) For what values of x is d smallest?
The graph of the function f(x) is shown below. It consists of a semicircle and two straight line segments. 50 -3 -2 y 3 2 -1 1 2 (a) Which of the following numbers is the largest: f'(-3.95), ƒ' (-1.5), ƒ' (-0.05), ƒ' (1), ƒ' (3.05)? 3 4 5 X
Sketch the graph of a function f which has the following characteristics. • f(3) = -4 • f'(x) 0 if x>3 f"(x)5 • f"(x) >0 if x < 5 lim f(x) =2
Prob. 6 (a) (10 point) Let f(x) = 2x² – 3. Find ƒ'(−2) using only the limit definition of derivatives. (b) (10 p.) If ƒ(x) = √√x + 6, find the derivative f'(c) at an arbitrary point c using only the limit definition of derivatives.
Suppose f is a function that satisfies all the following conditions. f'(x)>0 if -3 6; f"(x) = e2**7 if x0 if 0 6; lim f(x)=-15 and lim f (x)= 12%3; (ii) (iv) (v) (vi) X→ーの X→の f is continuous on (-o, o); f is not differentiable at x 3 and x 6; (vii) (viii) (ix) f (0) = f(6) = 0. Sketch a graph of the function f. Label the asymptote(s) and intercept(s) where %3D %3D applicable.
If f(x) = 3x² - x³, find f'(x), ƒ''(x), ƒ'''(x), and f(4)(x). f'(x) = f"(x) = f'(x) = f(4) (x) = Graph f, f', f", and f"" on a common screen. Are the graphs consistent with the geometric interpretations of these derivatives? The graphs ---Select--- consistent with the geometric interpretations of the derivatives because f' ---Select--- --Select--- ✓where f' has a slope of m = 0, and f"" is ---Select--- ✓function equal to the slope of f". ✓where f has a slope of m = 0, f"
The graph of y = f(x) is shown. Assume f'(x) is continuous. 8 7 6 5 4 3 2 1 8 -7 -6 -5 -3 -2 -1 Find xf(x) - 8 2 f(x) + x³ + 12 lim -3 -4 -5 -6 -7 -8. 1 2 3 4 5 6 7 8 o
4. (6 points) The function f is defined by f(x) = v25 – x² for -5 S x 5. (a) Find f(x). (b) Write an equation for the line tangent to the graph of f at x = -3. SS(x) for -5 sxs-3 (c) Let g be the function defined by g(x) = 'x + 7 for -3
Sketch a possible graph of f (r) that has the following properties f(x) 0 on (-00,-3) and (-3,1) f(x) 0 on (-00,-3), (0,1), and (1,co) "(x) <0 on(-3,0)
The derivative of the function f(x) = -822 f(x + h) – f(x) 12x + 25 by definition of derivatives f'(r) = lim %3D h -16x 12 -24x + 25 -8x -8x - 12 -16x
Sketch the graph of a function that satisfies all of the given conditions. (a) f'(x) < 0 and f"(x) < 0 for all x y y y X

SEE MORE QUESTIONS

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