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 local maxima or minima. What conclusions can be drawn?

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.

Some of Amber's daily activities are listed here. Use these descriptions to select the word or symbol that correctly completes each sentence. • Amber spends 3/16 of each day doing homework. • Amber spends 0.25 of each day at school. • Amber spends 1/3 of each day sleeping. (A) 3/16 of a day 0.25 of a day (B) 0.25 of a day 1/3 of a day (C) Amber spends time doing homework than she does at school. (D) Amber spends time sleeping than she does at school.

PLEASE ANSWER ASAP!!!!! :)

Claire jogs no more than 20 miles per week. Which inequality represents the number of miles she runs each week? A.x > 20 B.x < 20 C. x ≥ 20 D.x ≤ 20

Find the slope of the line passing through the points (3, 8) and (-2,5).
A.3/5
B.13
C.3

what are the statements and reasons?

What’s the y-intercept of the line?
A.1
B.(0,1)
C.(0,-1/2)
D. 1/2

What is 122.18 rounded to the nearest whole number?

in the box of decorations there are a number of four bubbles all of them are blue except for six of them are green except for six of them are red except for 6 how many bubbles do I have in total

1-sen^{4} x - cos^{4} x = 2sen^{2} x cos^{2} x

Tomas is planning out a rail trail using a map with a marked grid. The head of the trail, which has an information kiosk, is located at (3, 0). He moves 1 unit east and 3 units north and places a pin at (4, 3) to represent the location of another information kiosk. He continues to move 1 unit east and 3 units north twelve more times, placing a pin each time. Where will the last pin be placed?

Yesterday you wanted to make an enormous batch of rolls, so you
borrowed some special yeast from your aunt's top-secret bread
research facility. Once you mixed the yeast, flour, and water, the
dough began to double in volume every minute! After 13 minutes, at
exactly 5:53, your bowl was hali full. At what time will your bowl be
full of dough?

[tex] \frac{2}{6} + \frac{1}{8} [/tex]
help please I forgot how to do this​

------------------------------------------------------

Can u guys help me with 1a-1c

solve for w
5w+9z=2z+3w​

PLEASE ANSWER ILL GIVE POINTS:

if the product (2x + 3)(x + k) is 2x^2 + 13x + 15, what is the value of k?

Factor the polynomial completely
[tex]x {}^{2} + 2x - 63[/tex]
​

Find the value of y​

8 – 3(4x - 1) >= -49​

where can i read Mind If I Read Your Mind free

A robot can complete 4 tasks in 3/5 hour. Each task takes the same amount of time. a. How long does it take the robot to complete one​ task? b. How many tasks can the robot complete in one​ hour?

What is the slope for (2,-1) and (6, -1)

please help me! i will give brainliest!

A nearby school for wizardry is larger. They have 14 times as many students.
How many students attend the school for wizardry?

State the conclusion based on the results of the test. The standard deviationstandard deviation inin the pressure required to open a certain valve is known to be sigma equals 1.3 psi.σ=1.3 psi. Due to changes in the manufacturing​ process, the​ quality-control manager feels that the pressurepressure variabilityvariability has changedchanged. The null hypothesis was rejected.Choose the correct answer below. A. There is not sufficient evidence that the mean of the pressure required to open a certain valve has not changed. B. There is sufficient evidence that the mean of the pressure required to open a certain valve has changed. C. The mean of the pressure has not changed. D. The mean of the pressure has changed. E. There is sufficient evidence that the mean of the pressure required to open a certain valve has not changed. F. There is not sufficient evidence that the mean of the pressure required to open a certain valve has changed.

Francis has a large vegetable garden that covers 47 of her backyard. Her patio covers 13 of the yard, and the rest is grass. What portion of Francis’s yard is grass.

Coach Gannon Bought 8 Bags Of Sunflower Seeds For The Baseball Game. Each Bag Has 2 1/4 Cups Of Seeds. If Coach Gannon Has 12 Baseplayers On The Team, How Many Cups Of Seeds Can Each Player Have?

The next two terms of the sequence 4, 7, 10, 13 are ..

16 and 19
15 and 19
15 and 18
16 and 18

I think of a number, square it, then subtract the original number. The result is 30. What could the number be

what is the formula of mean ???? pls explain​