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
Dafna1 [17]
3 years ago
13

Find the intervals on which​ f(x) is​ increasing, the intervals on which​ f(x) is​ decreasing, and the local extrema. f (x )equa

ls 2 x cubed minus 15 x squared minus 216 x f(x)=2x3−15x2−216x
Mathematics
1 answer:
Kaylis [27]3 years ago
7 0

Answer:

f(x) is increasing in the intervals (-∞,-4) and (9,∞)

f(x) is decreasing in the ingercal (-4,9)

The local extrema is:

local max at (-4,496)

and local min at (9,-1701)

Step-by-step explanation:

In order to solve this problem we must start by finding the derivative of the provided function, which we can find by using the power rule.

if f(x)=ax^{n} then f'(x)=anx^{n-1}

so we get:

f(x)=2x^{3}-15x^{2}-216x

f'(x)=6x^{2}-30x-216

in order to find the critical points we mus set the derivative equal to zero, since the local max an min will happen when the slope of the tangent line to the given point is zero, so we get:

6x^{2}-30x-216=0

we can solve this by factoring, so let's factor that equation:

6(x+4)(x-9)=0

we can now set each of the factors equal to zero so we get:

x+4=0 and x-9=0

when solving each for x we get that:

x=-4 and x=9

These are our critical points, now we can build the possible intervals we are going to use to determine where the function will be increasing and where it will be decreasing:

(-∞,-4), (-4,9) and (9,∞)

so now we need to test these intervals in the derivative to see if the graph will be increasing or decreasing in the given intervals. So let's pick x=-5 for the first one, x=0 for the second one and x=10 for the third one.

When evaluating them into the first derivative we get that:

f'(-5)=84, this is a positive answer so it means that the function is increasing in the interval (-∞,--4)

f'(0)=-216, this is a negative anser so it means that the function is decreasing in the interval (-4,9)

f'(10)=84, this is a positive answer so it means that the function is increasing in the interval (9,∞)

Now, for the local extrema, we can see that at x=-4, the function it's increasing on the left of this point while it's decreasing to the right, which means that there will be a local maximum at x=-4, so the local max is the point (-4,496)

We can see that at x=9, the function it's decreasing on the left of this point while it's increasing to the right, which means that there will be a local minimum at x=-9, so the local min is the point (9,-1701)

You might be interested in
What is 15% of $150?'
AleksandrR [38]

Answer:

$22.50

Step-by-step explanation:

15% of 150=22.5

6 0
3 years ago
You are assigned by columbus high school to design a playground as part of your volunteer service. the playground consists of tw
Firlakuza [10]

Answer:

sorry

okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

4 0
1 year ago
Find the equation of the graphed line, please select the best answer from the choices provided.​
son4ous [18]

Answer: A

Step-by-step explanation: -2 is your y-int and if you do your rise over run it’s -1/2

7 0
3 years ago
One seal weights 22 pounds.Another seal weighs three thins. As much how much do the seals weigh altogether
ExtremeBDS [4]

Answer:

88 lbs

Step-by-step explanation:

22+22(3)=88

3 0
3 years ago
What percent of 25 is 12?
snow_lady [41]
12 * 4 = 48
25 * 4 = 100

48/100 = 0.48, or 48%

12 is 48% of 25
I hope this helps you

8 0
3 years ago
Read 2 more answers
Other questions:
  • Solve 8x-5&gt;or=27<br> Epic<br> Epic<br> Epic<br> Epic<br> Epic<br> Gamer momeent
    6·2 answers
  • Please answer this! I'll mark brainliest! &lt;3
    8·1 answer
  • Brad paints a house in 5 days. When his brother Nick joins him, they can paint a house in 3 days. How long does it take Nick to
    13·1 answer
  • Write the equation of the line graphed below.
    9·1 answer
  • (6.2N-8.3) +(9.1 + 1.4N)<br>​
    12·1 answer
  • Select the scenario below that demonstrates sampling bias. Select the correct answer below:
    14·1 answer
  • How do I do functions with graphs?
    12·1 answer
  • If the mean of m,n,s,p and q is 12. Calculate the mean of (m-4), (n-3 ),(s-6), (p-2) and (q-8).​
    10·1 answer
  • What is 0.25 ÷ 5.46 (show ur work)
    14·2 answers
  • Using principle of mathematical induction prove that 6^-1 divisble by 5 .​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!