   Chapter 3.R, Problem 18E

Chapter
Section
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

#### Find more solutions based on key concepts 