BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

17-28 Use the guidelines of Section 3.5 to sketch the curve.

y = 2 x 3 3 x 2 + 12 x + 5

To determine

To sketch:

The graph of the function y=-2x3-3x2+12x+5

Explanation

1) Concept:

i) A domain is the set of x values that satisfy the function.

ii) To find x-intercept, put y=0, and to find y-intercept, put x=0 in the given function.

iii) Symmetry: To find the symmetry, replace x by –x and check the behaviour of the function. Thus, if f-x=fx, then it is an even function, so it has y- axis symmetry, and if f-x=-fx, then it is an odd function, so it has x- axis symmetry. And if f-x-fxf(x) then it has no symmetry.

iv) An asymptote is a tangent at infinity. To find the horizontal, vertical and slant asymptotes, follow the rules.

v) Function is increasing if f'x>0  and decreasing if f'x<0 in that particular interval.

vi) The number f(c) has a local maximum value of f  if fcf(x) when x is near c, and a local minimum value of f if fc f(x) when x is near c.

vii) If f''x>0, the function is concave up and f''x<0, the function is concave down in that particular interval. And f''x=0 gives the values of inflection points

2) Given:

The function y=-2x3-3x2+12x+5

3) Calculation:

A) Domain

Since y=-2x3-3x2+12x+5  is a polynomial, its domain is -,  .

B) Intercepts

For the y- intercept, plug x=0  in the given function and solve it

y=-203-302+120+5=5

y intercept is (0, 5)

Next, for x-intercept, set y = 0 then the equation becomes

0=-2x3-3x2+12x+5

By using the graphing calculator x = -0.39, 2.04, -3.15

Therefore x-intercepts are -0.39,0, 2.04,0and (-3.15,0)

C) Symmetry

For symmetry, replace x by (-x), therefore,

f-x=-2-x3-3-x2+12-x+5=2x3-3x2-12x+5

Since, fxf-x or f-x-f(x)

That means there is no symmetry.

D) Asymptote

Also, (x+p)f(x); hence, f is not periodic

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started
Sect-3.1 P-11ESect-3.1 P-12ESect-3.1 P-13ESect-3.1 P-14ESect-3.1 P-15ESect-3.1 P-16ESect-3.1 P-17ESect-3.1 P-18ESect-3.1 P-19ESect-3.1 P-20ESect-3.1 P-21ESect-3.1 P-22ESect-3.1 P-23ESect-3.1 P-24ESect-3.1 P-25ESect-3.1 P-26ESect-3.1 P-27ESect-3.1 P-28ESect-3.1 P-29ESect-3.1 P-30ESect-3.1 P-31ESect-3.1 P-32ESect-3.1 P-33ESect-3.1 P-34ESect-3.1 P-35ESect-3.1 P-36ESect-3.1 P-37ESect-3.1 P-38ESect-3.1 P-39ESect-3.1 P-40ESect-3.1 P-41ESect-3.1 P-42ESect-3.1 P-43ESect-3.1 P-44ESect-3.1 P-45ESect-3.1 P-46ESect-3.1 P-47ESect-3.1 P-48ESect-3.1 P-49ESect-3.1 P-50ESect-3.1 P-51ESect-3.1 P-52ESect-3.1 P-53ESect-3.1 P-54ESect-3.1 P-55ESect-3.1 P-56ESect-3.1 P-57ESect-3.1 P-58ESect-3.1 P-59ESect-3.1 P-60ESect-3.1 P-61ESect-3.1 P-62ESect-3.1 P-63ESect-3.1 P-64ESect-3.1 P-65ESect-3.1 P-66ESect-3.1 P-67ESect-3.1 P-68ESect-3.1 P-69ESect-3.1 P-70ESect-3.1 P-71ESect-3.1 P-72ESect-3.2 P-1ESect-3.2 P-2ESect-3.2 P-3ESect-3.2 P-4ESect-3.2 P-5ESect-3.2 P-6ESect-3.2 P-7ESect-3.2 P-8ESect-3.2 P-9ESect-3.2 P-10ESect-3.2 P-11ESect-3.2 P-12ESect-3.2 P-13ESect-3.2 P-14ESect-3.2 P-15ESect-3.2 P-16ESect-3.2 P-17ESect-3.2 P-18ESect-3.2 P-19ESect-3.2 P-20ESect-3.2 P-21ESect-3.2 P-22ESect-3.2 P-23ESect-3.2 P-24ESect-3.2 P-25ESect-3.2 P-26ESect-3.2 P-27ESect-3.2 P-28ESect-3.2 P-29ESect-3.2 P-30ESect-3.2 P-31ESect-3.2 P-32ESect-3.2 P-33ESect-3.2 P-34ESect-3.2 P-35ESect-3.2 P-36ESect-3.3 P-1ESect-3.3 P-2ESect-3.3 P-3ESect-3.3 P-4ESect-3.3 P-5ESect-3.3 P-6ESect-3.3 P-7ESect-3.3 P-8ESect-3.3 P-9ESect-3.3 P-10ESect-3.3 P-11ESect-3.3 P-12ESect-3.3 P-13ESect-3.3 P-14ESect-3.3 P-15ESect-3.3 P-16ESect-3.3 P-17ESect-3.3 P-18ESect-3.3 P-19ESect-3.3 P-20ESect-3.3 P-21ESect-3.3 P-22ESect-3.3 P-23ESect-3.3 P-24ESect-3.3 P-25ESect-3.3 P-26ESect-3.3 P-27ESect-3.3 P-28ESect-3.3 P-29ESect-3.3 P-30ESect-3.3 P-31ESect-3.3 P-32ESect-3.3 P-33ESect-3.3 P-34ESect-3.3 P-35ESect-3.3 P-36ESect-3.3 P-37ESect-3.3 P-38ESect-3.3 P-39ESect-3.3 P-40ESect-3.3 P-41ESect-3.3 P-42ESect-3.3 P-43ESect-3.3 P-44ESect-3.3 P-45ESect-3.3 P-46ESect-3.3 P-47ESect-3.3 P-48ESect-3.3 P-49ESect-3.3 P-50ESect-3.3 P-51ESect-3.3 P-52ESect-3.3 P-53ESect-3.3 P-54ESect-3.3 P-55ESect-3.3 P-56ESect-3.3 P-57ESect-3.3 P-58ESect-3.3 P-59ESect-3.3 P-60ESect-3.3 P-61ESect-3.3 P-62ESect-3.3 P-63ESect-3.3 P-64ESect-3.3 P-65ESect-3.3 P-66ESect-3.3 P-67ESect-3.3 P-68ESect-3.3 P-69ESect-3.3 P-70ESect-3.3 P-71ESect-3.3 P-72ESect-3.3 P-73ESect-3.3 P-74ESect-3.3 P-75ESect-3.3 P-76ESect-3.3 P-77ESect-3.4 P-1ESect-3.4 P-2ESect-3.4 P-3ESect-3.4 P-4ESect-3.4 P-5ESect-3.4 P-6ESect-3.4 P-7ESect-3.4 P-8ESect-3.4 P-9ESect-3.4 P-10ESect-3.4 P-11ESect-3.4 P-12ESect-3.4 P-13ESect-3.4 P-14ESect-3.4 P-15ESect-3.4 P-16ESect-3.4 P-17ESect-3.4 P-18ESect-3.4 P-19ESect-3.4 P-20ESect-3.4 P-21ESect-3.4 P-22ESect-3.4 P-23ESect-3.4 P-24ESect-3.4 P-25ESect-3.4 P-26ESect-3.4 P-27ESect-3.4 P-28ESect-3.4 P-29ESect-3.4 P-30ESect-3.4 P-31ESect-3.4 P-32ESect-3.4 P-33ESect-3.4 P-34ESect-3.4 P-35ESect-3.4 P-36ESect-3.4 P-37ESect-3.4 P-38ESect-3.4 P-39ESect-3.4 P-40ESect-3.4 P-41ESect-3.4 P-42ESect-3.4 P-43ESect-3.4 P-44ESect-3.4 P-45ESect-3.4 P-46ESect-3.4 P-47ESect-3.4 P-48ESect-3.4 P-49ESect-3.4 P-50ESect-3.4 P-51ESect-3.4 P-52ESect-3.4 P-53ESect-3.4 P-54ESect-3.4 P-55ESect-3.4 P-56ESect-3.4 P-57ESect-3.4 P-58ESect-3.4 P-59ESect-3.4 P-60ESect-3.4 P-61ESect-3.4 P-62ESect-3.4 P-63ESect-3.4 P-64ESect-3.4 P-65ESect-3.4 P-66ESect-3.4 P-67ESect-3.4 P-68ESect-3.4 P-69ESect-3.4 P-70ESect-3.4 P-71ESect-3.4 P-72ESect-3.4 P-73ESect-3.4 P-74ESect-3.5 P-1ESect-3.5 P-2ESect-3.5 P-3ESect-3.5 P-4ESect-3.5 P-5ESect-3.5 P-6ESect-3.5 P-7ESect-3.5 P-8ESect-3.5 P-9ESect-3.5 P-10ESect-3.5 P-11ESect-3.5 P-12ESect-3.5 P-13ESect-3.5 P-14ESect-3.5 P-15ESect-3.5 P-16ESect-3.5 P-17ESect-3.5 P-18ESect-3.5 P-19ESect-3.5 P-20ESect-3.5 P-21ESect-3.5 P-22ESect-3.5 P-23ESect-3.5 P-24ESect-3.5 P-25ESect-3.5 P-26ESect-3.5 P-27ESect-3.5 P-28ESect-3.5 P-29ESect-3.5 P-30ESect-3.5 P-31ESect-3.5 P-32ESect-3.5 P-33ESect-3.5 P-34ESect-3.5 P-35ESect-3.5 P-36ESect-3.5 P-37ESect-3.5 P-38ESect-3.5 P-39ESect-3.5 P-40ESect-3.5 P-41ESect-3.5 P-42ESect-3.5 P-43ESect-3.5 P-44ESect-3.5 P-45ESect-3.5 P-46ESect-3.5 P-47ESect-3.5 P-48ESect-3.5 P-49ESect-3.5 P-50ESect-3.5 P-51ESect-3.5 P-52ESect-3.5 P-53ESect-3.5 P-54ESect-3.5 P-55ESect-3.5 P-56ESect-3.5 P-57ESect-3.5 P-58ESect-3.5 P-59ESect-3.5 P-60ESect-3.6 P-1ESect-3.6 P-2ESect-3.6 P-3ESect-3.6 P-4ESect-3.6 P-5ESect-3.6 P-6ESect-3.6 P-7ESect-3.6 P-8ESect-3.6 P-9ESect-3.6 P-10ESect-3.6 P-11ESect-3.6 P-12ESect-3.6 P-13ESect-3.6 P-14ESect-3.6 P-15ESect-3.6 P-16ESect-3.6 P-17ESect-3.6 P-18ESect-3.6 P-19ESect-3.6 P-20ESect-3.6 P-21ESect-3.6 P-22ESect-3.6 P-23ESect-3.6 P-24ESect-3.6 P-25ESect-3.6 P-26ESect-3.6 P-27ESect-3.6 P-28ESect-3.7 P-1ESect-3.7 P-2ESect-3.7 P-3ESect-3.7 P-4ESect-3.7 P-5ESect-3.7 P-6ESect-3.7 P-7ESect-3.7 P-8ESect-3.7 P-9ESect-3.7 P-10ESect-3.7 P-11ESect-3.7 P-12ESect-3.7 P-13ESect-3.7 P-14ESect-3.7 P-15ESect-3.7 P-16ESect-3.7 P-17ESect-3.7 P-18ESect-3.7 P-19ESect-3.7 P-20ESect-3.7 P-21ESect-3.7 P-22ESect-3.7 P-23ESect-3.7 P-24ESect-3.7 P-25ESect-3.7 P-26ESect-3.7 P-27ESect-3.7 P-28ESect-3.7 P-29ESect-3.7 P-30ESect-3.7 P-31ESect-3.7 P-32ESect-3.7 P-33ESect-3.7 P-34ESect-3.7 P-35ESect-3.7 P-36ESect-3.7 P-37ESect-3.7 P-38ESect-3.7 P-39ESect-3.7 P-40ESect-3.7 P-41ESect-3.7 P-42ESect-3.7 P-43ESect-3.7 P-44ESect-3.7 P-45ESect-3.7 P-46ESect-3.7 P-47ESect-3.7 P-48ESect-3.7 P-49ESect-3.7 P-50ESect-3.7 P-51ESect-3.7 P-52ESect-3.7 P-53ESect-3.7 P-54ESect-3.7 P-55ESect-3.7 P-56ESect-3.7 P-57ESect-3.7 P-58ESect-3.7 P-59ESect-3.7 P-60ESect-3.7 P-61ESect-3.7 P-62ESect-3.7 P-63ESect-3.7 P-64ESect-3.7 P-65ESect-3.7 P-66ESect-3.7 P-67ESect-3.7 P-68ESect-3.7 P-69ESect-3.7 P-70ESect-3.7 P-71ESect-3.7 P-72ESect-3.7 P-73ESect-3.7 P-74ESect-3.7 P-75ESect-3.7 P-76ESect-3.7 P-77ESect-3.7 P-78ESect-3.7 P-79ESect-3.7 P-80ESect-3.8 P-1ESect-3.8 P-2ESect-3.8 P-3ESect-3.8 P-4ESect-3.8 P-5ESect-3.8 P-6ESect-3.8 P-7ESect-3.8 P-8ESect-3.8 P-9ESect-3.8 P-10ESect-3.8 P-11ESect-3.8 P-12ESect-3.8 P-13ESect-3.8 P-14ESect-3.8 P-15ESect-3.8 P-16ESect-3.8 P-17ESect-3.8 P-18ESect-3.8 P-19ESect-3.8 P-20ESect-3.8 P-21ESect-3.8 P-22ESect-3.8 P-23ESect-3.8 P-24ESect-3.8 P-25ESect-3.8 P-26ESect-3.8 P-27ESect-3.8 P-28ESect-3.8 P-29ESect-3.8 P-30ESect-3.8 P-31ESect-3.8 P-32ESect-3.8 P-33ESect-3.8 P-34ESect-3.8 P-35ESect-3.8 P-36ESect-3.8 P-37ESect-3.8 P-38ESect-3.8 P-39ESect-3.8 P-40ESect-3.9 P-1ESect-3.9 P-2ESect-3.9 P-3ESect-3.9 P-4ESect-3.9 P-5ESect-3.9 P-6ESect-3.9 P-7ESect-3.9 P-8ESect-3.9 P-9ESect-3.9 P-10ESect-3.9 P-11ESect-3.9 P-12ESect-3.9 P-13ESect-3.9 P-14ESect-3.9 P-15ESect-3.9 P-16ESect-3.9 P-17ESect-3.9 P-18ESect-3.9 P-19ESect-3.9 P-20ESect-3.9 P-21ESect-3.9 P-22ESect-3.9 P-23ESect-3.9 P-24ESect-3.9 P-25ESect-3.9 P-26ESect-3.9 P-27ESect-3.9 P-28ESect-3.9 P-29ESect-3.9 P-30ESect-3.9 P-31ESect-3.9 P-32ESect-3.9 P-33ESect-3.9 P-34ESect-3.9 P-35ESect-3.9 P-36ESect-3.9 P-37ESect-3.9 P-38ESect-3.9 P-39ESect-3.9 P-40ESect-3.9 P-41ESect-3.9 P-42ESect-3.9 P-43ESect-3.9 P-44ESect-3.9 P-45ESect-3.9 P-46ESect-3.9 P-47ESect-3.9 P-48ESect-3.9 P-49ESect-3.9 P-50ESect-3.9 P-51ESect-3.9 P-52ESect-3.9 P-53ESect-3.9 P-54ESect-3.9 P-55ESect-3.9 P-56ESect-3.9 P-57ESect-3.9 P-58ESect-3.9 P-59ESect-3.9 P-60ESect-3.9 P-61ESect-3.9 P-62ESect-3.9 P-63ESect-3.9 P-64ESect-3.9 P-65ESect-3.9 P-66ESect-3.9 P-67ESect-3.9 P-68ESect-3.9 P-69ESect-3.9 P-70ESect-3.9 P-71ESect-3.9 P-72ESect-3.9 P-73ESect-3.R P-1CCSect-3.R P-2CCSect-3.R P-3CCSect-3.R P-4CCSect-3.R P-5CCSect-3.R P-6CCSect-3.R P-7CCSect-3.R P-8CCSect-3.R P-9CCSect-3.R P-10CCSect-3.R P-11CCSect-3.R P-1TFQSect-3.R P-2TFQSect-3.R P-3TFQSect-3.R P-4TFQSect-3.R P-5TFQSect-3.R P-6TFQSect-3.R P-7TFQSect-3.R P-8TFQSect-3.R P-9TFQSect-3.R P-10TFQSect-3.R P-11TFQSect-3.R P-12TFQSect-3.R P-13TFQSect-3.R P-14TFQSect-3.R P-15TFQSect-3.R P-16TFQSect-3.R P-17TFQSect-3.R P-18TFQSect-3.R P-19TFQSect-3.R P-1ESect-3.R P-2ESect-3.R P-3ESect-3.R P-4ESect-3.R P-5ESect-3.R P-6ESect-3.R P-7ESect-3.R P-8ESect-3.R P-9ESect-3.R P-10ESect-3.R P-11ESect-3.R P-12ESect-3.R P-13ESect-3.R P-14ESect-3.R P-15ESect-3.R P-16ESect-3.R P-17ESect-3.R P-18ESect-3.R P-19ESect-3.R P-20ESect-3.R P-21ESect-3.R P-22ESect-3.R P-23ESect-3.R P-24ESect-3.R P-25ESect-3.R P-26ESect-3.R P-27ESect-3.R P-28ESect-3.R P-29ESect-3.R P-30ESect-3.R P-31ESect-3.R P-32ESect-3.R P-33ESect-3.R P-34ESect-3.R P-35ESect-3.R P-36ESect-3.R P-37ESect-3.R P-38ESect-3.R P-39ESect-3.R P-40ESect-3.R P-41ESect-3.R P-42ESect-3.R P-43ESect-3.R P-44ESect-3.R P-45ESect-3.R P-46ESect-3.R P-47ESect-3.R P-48ESect-3.R P-49ESect-3.R P-50ESect-3.R P-51ESect-3.R P-52ESect-3.R P-53ESect-3.R P-54ESect-3.R P-55ESect-3.R P-56ESect-3.R P-57ESect-3.R P-58ESect-3.R P-59ESect-3.R P-60ESect-3.R P-61ESect-3.R P-62ESect-3.R P-63ESect-3.R P-64ESect-3.R P-65ESect-3.R P-66ESect-3.R P-67ESect-3.R P-68ESect-3.P P-1PSect-3.P P-2PSect-3.P P-3PSect-3.P P-4PSect-3.P P-5PSect-3.P P-6PSect-3.P P-7PSect-3.P P-8PSect-3.P P-9PSect-3.P P-10PSect-3.P P-11PSect-3.P P-12PSect-3.P P-13PSect-3.P P-14PSect-3.P P-15PSect-3.P P-16PSect-3.P P-17PSect-3.P P-18PSect-3.P P-19PSect-3.P P-20PSect-3.P P-21PSect-3.P P-22PSect-3.P P-23PSect-3.P P-24P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Convert the expressions in Exercises 31-36 to positive exponent form. 34x2/3

Finite Mathematics and Applied Calculus (MindTap Course List)

Find the mean for the following set of scores: 2, 7, 9, 4, 5, 3, 0, 6

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

What are the two requirements for a random sample?

Statistics for The Behavioral Sciences (MindTap Course List)

If the line passing through the points (a, 1) and (5, 8) is parallel to the line passing through the points (4,...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Solve each inequality. 02x+342

Trigonometry (MindTap Course List)

Which is true about the series ? diverges converges absolutely converges conditionally converges, but not absol...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th