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
tensa zangetsu [6.8K]
2 years ago
5

How do you find the absolute extrema of this function? f(x) = x+3x^(2/3); Interval is [-10,1]

Mathematics
1 answer:
Step2247 [10]2 years ago
8 0
\bf f(x)=x+3x^{\frac{2}{3}}\implies \cfrac{dy}{dx}=1+3\left(\frac{2}{3}x^{-\frac{1}{3}}  \right)\implies \cfrac{dy}{dx}=1+\cfrac{2}{\sqrt[3]{x}}
\\\\\\
\cfrac{dy}{dx}=\cfrac{\sqrt[3]{x}+2}{\sqrt[3]{x}}\implies 0=\cfrac{\sqrt[3]{x}+2}{\sqrt[3]{x}}\implies 0=\sqrt[3]{x}+2\implies -2=\sqrt[3]{x}
\\\\\\
(-2)^3=x\implies \boxed{-8=x}\\\\
-------------------------------\\\\
0=\sqrt[3]{x}\implies \boxed{0=x}

now, f(0) = 0, and f(-8) is an imaginary value or no real value.

now, f(-10)   will also give us an imaginary value

and f(1) = 4

so, doing a first-derivative test on 0, is imaginary to the left and positive on the right, and before and after 1, is positive as well, so f(x) is going up on those intervals.

however, f(0) is 0 and f(1) is higher up, so the absolute maximum will have to be f(1), and we can use f(0) as a minimum, and since it's the only one, the absolute minimum.

the other two, the endpoint of -10 and the critical point of -8, do not yield any values for f(x).
You might be interested in
Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are common catches. The mean length of
julia-pushkina [17]

Answer:

Due to the higher z-score, Stewart caught the longer fish, relative to fish of the same species

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Who caught the longer fish, relative to fish of the same species?

Whosoever fish's had the higher z-score.

Stewart caught a bluefish that was 283mm

The mean length of a bluefish is 264 millimeters with a standard deviation of 57mm.

So we have to find Z when X = 283, \mu = 264, \sigma = 57

Z = \frac{X - \mu}{\sigma}

Z = \frac{283 - 264}{57}

Z = 0.33

Gina caught a pompano that was 152mm long.

For pompano, the mean is 157mm with a standard deviation of 28mm.

So we have to find Z when X = 152, \mu = 157, \sigma = 28

Z = \frac{X - \mu}{\sigma}

Z = \frac{152 - 157}{28}

Z = -0.18

Due to the higher z-score, Stewart caught the longer fish, relative to fish of the same species

8 0
3 years ago
A recipe requires 1/2 cup of milk and 1/3 cup of water. How much more milk is required for the recipe water?
Lapatulllka [165]

1/2-1/3

(1/2)x3-(1/3)x2

3/6-2/6

1/6

7 0
3 years ago
SOMEONE HELP ME!!!! ILL MAKE MOST BRAINLIEST PLEASE HELP
tigry1 [53]
= 2^-16 * 3^10 *3^-8/ 2^12 * 2^28
= 2^(-16 - 12 + 28) * 3^(10 - 8)
= 2^0 * 3^2
= 9

answer
9
4 0
3 years ago
Read 2 more answers
I will give brainliest, if it is right, and you are the first person to answer.
sertanlavr [38]

Answer:47.25

Step-by-step explanation: it is 10.5 x the 4.5

7 0
2 years ago
Read 2 more answers
6. I NEED HELP ASAP!! PLEASE PUT AND ANSWER AND STEP BY STEP EQUATION!! IF YOU DON'T KNOW THE ANSWER DON'T PUT ANYTHING!!
kramer

Answer:

I think the answer is B. f(x) = -1/3x - 4

Step-by-step explanation:

Use the given functions to set up and simplify  

4−16.

XF(x)=X

Fx

1 − 7 = −6

2 − 10 = −8

3 − 13 = −10

4 − 16 = −12

8 0
2 years ago
Other questions:
  • Can some one help me with this?????
    13·2 answers
  • What is the area of the figure? How do you find it?
    8·1 answer
  • 4^n=16 <br> Can someone please help me answer this question ?
    14·1 answer
  • Between x = 2 and x = 3, which function has a greater average rate of change than y = 13 -x ?
    5·1 answer
  • Needing a answer ASAP! TYYY
    15·2 answers
  • Can u help me <br><br>thanks u
    5·1 answer
  • Can someone help me thankyou &lt;3
    7·1 answer
  • judy borrow 600 from her friend and promises to pay it back in 3 years with the 4% interest rate. calculate the simple interest
    14·1 answer
  • Which of the equations below could be the equation of this parabola? (0, 0) A. x= - 1 / 4y² B. x=-1/4x2 C. x=1/4y2 D. x=1/4x2​
    11·1 answer
  • A pair of shoes is on sale for $51, which is a 25%
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!