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
Which expersstion is equevelint to (6xp) + 3?
nikitadnepr [17]

Answer:

3+(px6)

Step-by-step explanation:

3 0
3 years ago
How many triangles can be constructed with angles measuring 50º, 90º, and 40º?
IRINA_888 [86]
A triangles angles all add up to 180*. so 90*+50*+40*=180*
8 0
3 years ago
Read 2 more answers
The depths of three different submarines are listed below. Which of the following statements are true? Choose all that apply.
AnnZ [28]
The correct answer choices are B and C.

Here is the way these numbers would fall on a vertical number line justifying why these 2 answers are correct.

-1500 A
-1600
-1700
-1800
-1900 B
-2000
-2100
-2200
-2300  C

You can see where each of these submarines is located.  0 is sea level.
7 0
3 years ago
Item 11 In the table, Pattern A uses the rule "add 5" and Pattern B uses the rule "add 10." Pattern A 10 15 20 25 30 Pattern B 2
Elena L [17]

The Pattern B is the twice of the Pattern A.  Then the correct option is C.

<h3>What is Algebra?</h3>

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Item 11 In the table,

Pattern A uses the rule "add 5" and Pattern B uses the rule "add 10".

Pattern A   10  15  20  25  30

Pattern B   20 30 40  50  60

Then the Pattern B is the twice of the Pattern A.

Then the correct option is C.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ1

7 0
2 years ago
find the equation of the line graph below in point slope form. show your work. (will make brainiest.)
Archy [21]
What line i really dont see nothing
5 0
3 years ago
Other questions:
  • Is 2/3 equal to 2/4 because the numerator are equal
    8·1 answer
  • 11 identical pairs of Air Jordan cost $660.What is the cost of one pair?
    15·1 answer
  • Verbal expression for 7^8
    7·2 answers
  • Which expression is equivalent to √128x^5y^6/2x^7y^5? Assume x&gt;0 and y&gt;0.
    6·2 answers
  • What is the whole number that is equal to 8/2
    15·2 answers
  • If a1 = 4 and an = (an-1)2 + 3 then find the value of a4.
    10·1 answer
  • ∠A is complementary to ∠B. The measure of ∠A is (8x+12)∘. The measure of ∠B is half the measure of ∠A.
    5·2 answers
  • Solve each linear system by Elimination. 2x + 3y =2, 4x-2y=4
    12·1 answer
  • Does anyone know the correct answer? Btw happy thanksgiving :-)
    13·2 answers
  • Anyone for a brainly help me out
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!