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
fomenos
3 years ago
14

Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x)= 6x^1/3 + 3x^4/3. You must justify

your answer using an analysis of f'(x) and f''(x)
My work so far
F'(x) =2/(x^2/3) + 4x^1/3
​
Mathematics
1 answer:
irina [24]3 years ago
7 0

Answer:

x-coordinates of relative extrema = \frac{-1}{2}

x-coordinates of the inflexion points are 0, 1

Step-by-step explanation:

f(x)=6x^{\frac{1}{3}}+3x^{\frac{4}{3}}

Differentiate with respect to x

f'(x)=6\left ( \frac{1}{3} \right )x^{\frac{-2}{3}}+3\left ( \frac{4}{3} \right )x^{\frac{1}{3}}=\frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}

f'(x)=0\Rightarrow \frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}=0\Rightarrow x=\frac{-1}{2}

Differentiate f'(x) with respect to x

f''(x)=2\left ( \frac{-2}{3} \right )x^{\frac{-5}{3}}+\frac{4}{3}x^{\frac{-2}{3}}=\frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}\\f''(x)=0\Rightarrow \frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}=0\Rightarrow x=1

At x = \frac{-1}{2},

f''\left ( \frac{-1}{2} \right )=\frac{4\left ( -1+4\left ( \frac{-1}{2} \right ) \right )}{3\left ( \frac{-1}{2} \right )^{\frac{5}{3}}}>0

We know that if f''(a)>0 then x = a is a point of minima.

So, x=\frac{-1}{2} is a point of minima.

For inflexion points:

Inflexion points are the points at which f''(x) = 0 or f''(x) is not defined.

So, x-coordinates of the inflexion points are 0, 1

You might be interested in
What is 166.44 dived by 4. PLEASE USE LONG DIVISION. The person who USES LONG DIVISION TO GET THE ANSWER GETS 10 points and brai
ArbitrLikvidat [17]

Answer:

41.61

Step-by-step explanation:

Just divide.

\begin{matrix}4\overline{|\smallspace166.44}\:\:\:\:\:\:\:\end{matrix}


5 0
1 year ago
Read 2 more answers
Doesn't 1 foot and 6 inches equal 1 1/2 of a foot??? I'm just d u m b. Don't ask why I'm asking one of the most S T U P I D E S
Assoli18 [71]

Answer:

Well your answer is yes, and you shouldn't be calling yourself d u m b

Step-by-step explanation:

(By the way, I would love Brainliest! :)

4 0
3 years ago
Read 2 more answers
I WILL AKE YOU THE BRAINLIEST EASY QUESTION
avanturin [10]

Answer:

3rd choice

Step-by-step explanation:

9/5 = 18/10 = 1.8

All your numbers are between 1 and 2, and all have a fractional part that is a whole number of tenths. 1.3, 1.5, and 1.8 will be correctly shown by dots on the 3rd, 5th, and 8th marks.

6 0
3 years ago
Read 2 more answers
A ball is thrown into the air from the roof of a building that is 25
guapka [62]

See https://web2.0calc.com/questions/help_29603.

6 0
3 years ago
the distant around a track is 1/4 mile. a marathon is 26 1/5 miles. How many laps does it take to run a marathon​
sleet_krkn [62]

Answer:

108 1/8

Step-by-step explanation:

1/4=0.25, 1/5=0.2

=>26+0.2=26.2

=>26.2/0.25=108.8

8 0
3 years ago
Other questions:
  • Write decimal 3.4 as a fraction or a mixed number in simplesy form
    8·1 answer
  • Six men completed a task in 24 hrs and 48 min. How long, in hours and minutes, would it take four men to complete the same task?
    15·1 answer
  • How do u do order of operations
    14·2 answers
  • How do you use a unit circle?
    15·1 answer
  • A family is taking a cross country trip by car. They drive at an average speed of 55/mi/h, and their goal is to travel at least
    8·1 answer
  • The measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle.
    11·2 answers
  • Y=6/5x+9 in standard form
    13·1 answer
  • 1.What is (f-g)(x) ?<br> f(x)=x^4-3x^2+5x-7<br> g(x)= x^3-3x^2+3x-1
    12·1 answer
  • Which number has an absolute value greater than 4?
    14·1 answer
  • The following table represents the sample space of rolling two number cubes. 1 2 3 4 5 6 1 1-1 1-2 1-3 1-4 1-5 1-6 2 2-1 2-2 2-3
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!