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Dvinal [7]
3 years ago
5

Can someone help me with this question?

Mathematics
1 answer:
belka [17]3 years ago
4 0
Option 3 (1/4 x 60) since 59 is close to 60 and 25% can be rewritten as 1/4
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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
irina [24]

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

7 0
3 years ago
HURRY PLZ Four friends are collecting money to buy dog food for an animal shelter. The food will cost $150, and each friend will
satela [25.4K]

Four Friends Collecting money to buy Dog Food:

Food Cost $150.00

Each Friend Collect the Same amount of Money:  $37.50 each Collected

Just Divide:

$150.00   Divide amongst the  4  friends:

150.00/4

150/4       =      75/2

Answer  ======>   Decimal:    $37.50    Each friend would need to collect to reach their goals.


Check:

$37.50    *     4  

$150.00

150/4   =====>   $37.50





Hope that helps!!!!!!!!!                                                 : )






Hope that helps!!!                                             : )

3 0
3 years ago
Angle B measures 60°. What is the measure of the angle that is complementary to angle B? 30° 60° 120° 180°
Ivenika [448]

Answer:

30

Step-by-step explanation:

Complementary angle to B = 90 - 60 = 30

8 0
3 years ago
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Scores on a history test have average of 80 with standard deviation of 6. What is the z-score for a student who earned a 74 on t
Olegator [25]

Answer:

12

Step-by-step explanation:

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2 years ago
Im in school and u..
labwork [276]

Answer:

Online school, it sucks.

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2 years ago
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