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
earnstyle [38]
3 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]3 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.

You might be interested in
My mom died can u help me
nata0808 [166]

Answer: 5 minutes

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Laura is saving money to buy a bike. She has $52 and is going to save an additional $8 each week. The bike costs $164. In how ma
Montano1993 [528]
14 weeks
164-52=112
112/8=14
8 0
3 years ago
Read 2 more answers
Can someone help me on this math question pls I have 12 more questions I need help on too !
love history [14]

A is the answer. Since they will both be divided by 4 due to the same amount of points, because Globrite has a greater range, it will have a greater mean. Glo brite also ranges bigger than Luminate

5 0
3 years ago
The profitability, P, of a popular restaurant franchise can be modeled by the function P (t) = t4 – 10t3 + 28t2 – 24t, where t i
vekshin1

In this question, the profit of the restaurant after t months is given by a polynomial function. To find when it begins to show a profit, we find the numerical values of the function for t, and it shows a profit when t > 0

Profit after t months:

P(t) = t^4 - 10t^3 + 28t^2 - 24t

0 months:

This is P(0). So

P(0) = 0^4 - 10*0^3 + 28*0^2 - 24*0 = 0

1 month:

This is P(1). So

P(1) = 1^4 - 10*1^3 + 28*1^2 - 24*1 = -5

2 months:

This is P(2). So

P(2) = 2^4 - 10*2^3 + 28*2^2 - 24*2 = 0

3 months:

This is P(3). So

P(3) = 3^4 - 10*3^3 + 28*3^2 - 24*3 = -9

4 months:

This is P(4). So

P(4) = 4^4 - 10*4^3 + 28*4^2 - 24*4 = -32

5 months:

This is P(5). So

P(5) = 5^4 - 10*5^3 + 28*5^2 - 24*5 = -45

6 months:

This is P(6). So

P(6) = 6^4 - 10*6^3 + 28*6^2 - 24*6 = 0

7 months:

This is `P(7). So

P(7) = 7^4 - 10*7^3 + 28*7^2 - 24*7 = 175

After 7 months it shows profit, so it starts showing profit on the 6th month, and thus, the correct answer is given by option D.

For another example of a function involving numeric value, you can check brainly.com/question/24231879

8 0
3 years ago
How can using reciprocals help you divide fractions
tresset_1 [31]
When you divide fractions, you change each to its reciprocal, then you look multiply them. Using reciprocals helps you easily solve the problem.
7 0
3 years ago
Other questions:
  • Jonathon worked at McDonald's 20 hours per week and earned $195.Use the equation 20h=195 to find Komathons hourly wage.
    9·2 answers
  • Simplify 11/66 12/24 what is the answer
    7·2 answers
  • Help. Only #21 thanks
    13·1 answer
  • Three times a number increased by ten is equal to twenty less than six times the number. Find the number
    7·1 answer
  • This website is useless dont get any type of answers
    10·1 answer
  • THIS IS A K12 QUESTION WILL GIVE BRAINLIEST NEED ANSWER NOW!!!! For which distributions is the median the best measure of the ce
    7·2 answers
  • Halp halp halp meee <br> I give brain list to best answer pwease halp
    10·2 answers
  • How to solve x-6&gt;3 iheflweflwejmf;eaflnef;nqmqe;fmawfmqw;fm;qegm;wrgm;qemf;qfwm;qefm;qefm;wfm;qem;lqem;lemle
    8·1 answer
  • Janice Went to five different stores in the mall, she spent an average of $30 at each store. After visiting just the first four
    6·1 answer
  • What is the general equation of a sine function with an amplitude of 2, a period of Pi and a horizontal shift of Pi units? y = 2
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!