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earnstyle [38]
2 years ago
14

Use a graphing calculator to graph f(x) = x+cos(kx). Use calculus to determine which values of k lead to a function with no loca

l maxima or minima. What conclusions can be drawn?
Mathematics
1 answer:
nataly862011 [7]2 years ago
7 0

Answer:

Below, you can see the graph of the function:

f(x) = x + cos(k*x)

for different values of k, as follows:

red: k = 1

green: k = 2

orange: k = 0.

Now let's find the values of k such that our function does not have local maxima nor local minima.

First, remember that for a given function f(x), the local maxima or minima points are related to the zeros of the first derivate of f(x).

This means that if:

f'(x0) = 0.

Then x0 is a maxima, minima or an inflection point.

Then if a function is such that the f'(x) ≠ 0 , ∀x, then this function will not have local maxima nor minima.

Now we have:

f(x) = x + cos(k*x)

then:

f'(x) = 1  - k*sin(k*x)

This function will be zero when:

1 = k*sin(k*x)

1/k = sin(k*x)

now, remember that -1 ≤ sin(θ) ≤ 1

then if 1/k is smaller than -1, or larger than 1, we will not have zeros.

And this will happen if -1 < k < 1.

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Can You guys help me on these problems
klio [65]

Answer:

5=100

6=900

8=375

Step-by-step explanation:

LxWxH

20x4

300x3

5x5=25 x 15= 375

4 0
2 years ago
Origin, one of the four characteristics of mapping rules, refers to _____. the use of a number that is not used again the use of
labwork [276]

Answer:

the use of a series of numbers with a unique origin indicated by the number zero.

Step-by-step explanation:

In Science, mapping experiment refers to an investigation which typically involves the process of manipulating an independent variable (the cause) in order to be able to determine or measure the dependent variable (the effect).

This ultimately implies that, an experiment can be used by scientists to show or demonstrate how a condition causes or gives rise to another i.e cause and effect, influence, behavior, etc in a sample.

Origin, one of the four characteristics of mapping rules, refers to the use of a series of numbers with a unique origin indicated by the number zero.

In Mathematics, the origin is generally chosen to start from zero on a graph that gives the relationship between two variables.

4 0
2 years ago
Gradpoint-What is the value of y?<br><br>25<br><br>35<br><br>50<br><br>100
stepan [7]

Answer:

gradpoint what is the value of y look at the chart shown above a calculator maybbe needed

8 0
3 years ago
A middle schooler took all the 6th grader on a field trip to see ballet. The students filled up 570 seats, which was 95% of the
Musya8 [376]

The total  number of seats in the theater is 600 seats, if the students filled up 570 seats, which was 95% of the total number of seats in the theater.

Step-by-step explanation:

The given is,

                 Seats filled by students are 570 seats

                 Which is 95% of the total number of seats in the theater

Step: 1

                Let, x - Total number of seats available in theater

                Percentage of seats filled, y= 95%

                Seats filled by students = 570

                Formula to calculate total number of seats in theater,

                          95% of seats  = \frac{95}{100}( x)    

                                         570 = 0.95 (x)

                                              x = \frac{570}{0.95}

                                                 = 600

                                              x = 600 seats

Step: 2

            Check for solution,

                            5% of seats  = \frac{5}{100} (600)

                                                  = (0.05 × 600)

                                                  = 30 seats

                    Total no. of seats = 5% of seats  + 95% of seats

                                                  = 30 + 570

                                         600 = 600

Result:

           The total  number of seats in the theater is 600 seats.

7 0
3 years ago
Find y if 1030404(3y+36) = 1030403(3y+36).
Blababa [14]

Answer:

y= - 12

Step-by-step explanation:

7 0
3 years ago
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