Sketch the graphs of the following functions. 9. f(x)=x³-6x² + 12x-6 10. f(x) = -x³ 12. f(x)= x³ + 2x² + 4x 14 Mlad 2.3. 11. f(x)=x³ + 3x + 1 13. f(x)=513x + 6x²-x³
Sketch the graphs of the following functions. 9. f(x)=x³-6x² + 12x-6 10. f(x) = -x³ 12. f(x)= x³ + 2x² + 4x 14 Mlad 2.3. 11. f(x)=x³ + 3x + 1 13. f(x)=513x + 6x²-x³
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...
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Excercise 2.4 Q9,Q11&Q13 needed Please solve all questions in the order to get positive feedback These are easy questions you must have to solve all please By Hans solution needed only
![23. y
Sketch the graphs of the following functions.
9. f(x)=x³-6x² + 12x - 6
10. f(x) = -x³
12. f(x)= x³ + 2x² + 4x
14. f(x)=2x³ + x-2
16. f(x)=-3x³-6x²-9x-6
17. f(x)=1-3x+3x²-x³
18. f(x)=x³2x2go
19. f(x)=x4-6x²
21. f(x)=(x-3)4
COPY
Check Your Understanding 2.4
Determine whether each of the following functions has an asymp-
tote as x gets large. If so, give the equation of the straight line that
is the asymptote.
EXERCISES 2.4
Find the x-intercepts of the given function.pindosT
1. y=x²-3x+1
2. y = x? +5x+5
3. y = 2x² + 5x + 2
4. y=4-2x-x²
5. y = 4x - 4x²-10-
6. y = 3x² + 10x + 3
7. Show that the function f(x)= x³ - 2x² + 5x has no relative
extreme points shod Hames wh
8. Show that the function f(x) = -x³ + 2x2 - 6x + 3 is always
decreasing.
4ooo ads
9
25. y=+x+1
itions of the Derivative
² + ² + 2
0-1
=
27. y==+=
bauol 2
x 5
28. y = 12 +4-0
29. y = 6√x-x
A yol olg
(d) Look for possible asymptotes.
(1)
Sketch the graphs of the following functions for x > 0.
1 1
-+-
+=x
x
(e) Complete the sketch.
Examine the formula for f(x). If some terms become insignificant as x
gets large, and if the rest of the formula gives the equation of a straight
line, then that straight line is an asymptote.
(ii) Suppose that there is some point a such that f(x) is defined for x near a,
but not at a (for example, 1/x at x = 0). If f(x) gets arbitrarily large (in
the positive or negative sense) as x approaches a, the vertical line x = a is
an asymptote for the graph.
11. f(x)= x³ + 3x + 1
13. f(x)=513x + 6x²-x³
15. f(x)=x³2x² + x
20. f(x) = 3x4-6x² + 3
22. f(x) = (x+2)4 - 1
nota 30. y=
2
24. y=-
x
12
26. y=+ 3x + 1
x
[Hint: (1, 0) is an x-intercept.]
√x 2
3
1. f(x)==-2x+1
In Exercises 31 and 32, determine which function is the derivative
of the other.
31.
f(x)
32.
Box)
Solutions can be found following the section exercises.
2. f(x)=√x+x 3. f(x) = -1/2
g(x)
ing
200
31
ve
Y
laog ad folg bas
33. Find the quadratic function f(x) = ax² + bx+c that goes
(d) through (2,0) and has a local maximum at (0, 1).
34. Find the quadratic function f(x) = ax² + bx+c that goes
through (0, 1) and has a local minimum at (1,-1).
35. If f'(a) = 0 and f'(x) is increasing at x = a, explain why f(x)
must have a local minimum at x = a. [Hint: Use the first-
derivative test.]
36. If f'(a) = 0 and f'(x) is decreasing at x = a, explain why f(x)
must have a local maximum at x = a.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe83b972a-c189-49af-9357-b08dbf716629%2F33a60d5b-b749-4aba-8840-0791af010c66%2Fd6ilvog_processed.jpeg&w=3840&q=75)
Transcribed Image Text:23. y
Sketch the graphs of the following functions.
9. f(x)=x³-6x² + 12x - 6
10. f(x) = -x³
12. f(x)= x³ + 2x² + 4x
14. f(x)=2x³ + x-2
16. f(x)=-3x³-6x²-9x-6
17. f(x)=1-3x+3x²-x³
18. f(x)=x³2x2go
19. f(x)=x4-6x²
21. f(x)=(x-3)4
COPY
Check Your Understanding 2.4
Determine whether each of the following functions has an asymp-
tote as x gets large. If so, give the equation of the straight line that
is the asymptote.
EXERCISES 2.4
Find the x-intercepts of the given function.pindosT
1. y=x²-3x+1
2. y = x? +5x+5
3. y = 2x² + 5x + 2
4. y=4-2x-x²
5. y = 4x - 4x²-10-
6. y = 3x² + 10x + 3
7. Show that the function f(x)= x³ - 2x² + 5x has no relative
extreme points shod Hames wh
8. Show that the function f(x) = -x³ + 2x2 - 6x + 3 is always
decreasing.
4ooo ads
9
25. y=+x+1
itions of the Derivative
² + ² + 2
0-1
=
27. y==+=
bauol 2
x 5
28. y = 12 +4-0
29. y = 6√x-x
A yol olg
(d) Look for possible asymptotes.
(1)
Sketch the graphs of the following functions for x > 0.
1 1
-+-
+=x
x
(e) Complete the sketch.
Examine the formula for f(x). If some terms become insignificant as x
gets large, and if the rest of the formula gives the equation of a straight
line, then that straight line is an asymptote.
(ii) Suppose that there is some point a such that f(x) is defined for x near a,
but not at a (for example, 1/x at x = 0). If f(x) gets arbitrarily large (in
the positive or negative sense) as x approaches a, the vertical line x = a is
an asymptote for the graph.
11. f(x)= x³ + 3x + 1
13. f(x)=513x + 6x²-x³
15. f(x)=x³2x² + x
20. f(x) = 3x4-6x² + 3
22. f(x) = (x+2)4 - 1
nota 30. y=
2
24. y=-
x
12
26. y=+ 3x + 1
x
[Hint: (1, 0) is an x-intercept.]
√x 2
3
1. f(x)==-2x+1
In Exercises 31 and 32, determine which function is the derivative
of the other.
31.
f(x)
32.
Box)
Solutions can be found following the section exercises.
2. f(x)=√x+x 3. f(x) = -1/2
g(x)
ing
200
31
ve
Y
laog ad folg bas
33. Find the quadratic function f(x) = ax² + bx+c that goes
(d) through (2,0) and has a local maximum at (0, 1).
34. Find the quadratic function f(x) = ax² + bx+c that goes
through (0, 1) and has a local minimum at (1,-1).
35. If f'(a) = 0 and f'(x) is increasing at x = a, explain why f(x)
must have a local minimum at x = a. [Hint: Use the first-
derivative test.]
36. If f'(a) = 0 and f'(x) is decreasing at x = a, explain why f(x)
must have a local maximum at x = a.
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