1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sophie [7]
3 years ago
10

Require full steps working for this question

Mathematics
1 answer:
Ray Of Light [21]3 years ago
6 0

I let the computer do the graphing.  

f(x) = x(x + 3)²(1 - x) / 3

We see obvious zeros at x=0, x=-3 and x=1.

f(x) = x(x + 3)²(1 - x) / 3

f(x) = x(x^2 + 6x + 9)(1 - x)/3

f(x) = x(x^2 + 6x + 9 - x^3 - 6x^2 - 9x)/3

f(x) = x(- x^3 - 5x^2 -3x +9)/3

f(x) = (-x^4 - 5x^3 -3x^2 +9x)/3

f'(x) = (-4x^3 - 15x^2 -6x + 9)/3

We know there's f'(-3)=0 so x+3 must be a factor here,

f'(x) = (x + 3) (-4x^2 - 3x + 3)

We get stationary points when x = -3 or

x = (-1/8)( 3 ± √(9 - 4(-4)(3))) =  (-3 ± √57)/8  about -1.3 and 0.6 which are a local minimum and maximum respectively.

f''(x) = (-12x^2 - 30x -6)/3 = -4x^2 - 10x - 2

f''(-3) = -4(9)+ 30 - 2 = -8

Concave Down, Negative.   (-3,0) is a local maximum.

f''((-3 - √57)/8) = -4(-1.3)^2 - 10(-1.3) - 2 = 4.24

Concave up, positive, a CUP

(-3 - √57)/8, f((-3 - √57)/8) ) is a minimum.

f''((-3 + √57)/8) = -4(.6)^2 - 10(.6) - 2 = -9.44

CDN, ( ((-3 + √57)/8), f((-3 + √57)/8) ) is a maximum.

I didn't evaluate f((-3 ±√57)/8) which are around -3 and 1 but I leave that calculation to you.

You might be interested in
Ms. Simpson gives her class the following problem:Simplify: 3 (x-2) + 6x. Mikey
Schach [20]

Answer:

first off, when did Marge become a teacher

Step-by-step explanation:

Second off, he didn't flip the sign inside of the parentheses.

3 0
3 years ago
Read 2 more answers
What is the point-slope form equation of the graph?
sammy [17]

Answer:

y-4= 1/2(x+2)

Step-by-step explanation:

6 0
3 years ago
Jan is 2/3 of Karyn's age. Jan's age 8 years ago is 2/5 of Katyn's age 4 yeats from now. Jan is how many younger than Karyn?
Elden [556K]

Answer:

12 years younger.

Step-by-step explanation:

Let Jan's age be J and Karyn's age be K.

J= \frac{2}{3}  K

Jan's age 8 years ago is 2/5 of Karyn's age 4 yeaRs from now.

J-8 = \frac{2}{5} (K+4)

=> (\frac{2}{3} - \frac{2}{5} ) K = \frac{8}{5} + 8

=> 4K = 48 X 3

=> K= 36.

=> J= 24.

So Jan is 12 years younger.

8 0
3 years ago
Simplify square root of negative 48
77julia77 [94]
\bf \sqrt{-48}\qquad 
\begin{cases}
48=2\cdot 2\cdot 2\cdot 2\cdot 3\\
\qquad 2^2\cdot 2^2\cdot 3\\
\qquad (2^2)^2\cdot 3
\end{cases}\implies \sqrt{-1\cdot (2^2)^2\cdot 3}
\\\\\\
\sqrt{-1}\cdot \sqrt{(2^2)^2\cdot 3}\implies i\cdot 2^2\sqrt{3}\implies 4\sqrt{3}\ i
5 0
3 years ago
$70 plus a 5% tax and a 15% tip
Serjik [45]

Answer:

maybe 88.5

Step-by-step explanation:

calculator is god

5 0
2 years ago
Other questions:
  • Vf²=vi²+ 2ad <br><br> A) solve for vi<br><br> B) solve for d <br><br> Using the same equation
    15·1 answer
  • SHOW WORK PLEASEEE 18 POINTS
    12·2 answers
  • 2/3 of all the people who attended a certain party arrived by 8:00 PM. How many people arrived by 8:00 PM?
    14·1 answer
  • Please help :) Is the relationship shown by the data linear? If so model the data with an equation.
    9·1 answer
  • What function equation is represented by the graph? f(x)=14x+3 f(x)=−4x−3 f(x)=−14x−3 f(x)=14x−3
    10·2 answers
  • Can someone please help me with this
    13·1 answer
  • Choose an object that could be about the same length as each measurement.
    9·1 answer
  • 10. A bag contains 3 red marbles and 4 blue marbles. Two marbles are drawn at
    12·1 answer
  • A sofa is priced at $661.50. There is an 8% sales tax rate. What is the sales tax for the sofa in dollars and cents?
    5·1 answer
  • Resolver para x <br><br> 141-x=291
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!