determine the values of a and b which would resukt in the function f(x) being differentiable at x=4
Answers
The values of a and b that make the function differentiable are given as follows:
a = -7/6, b = -3/16.
What are the conditions for the function to be differentiable?The piece-wise function has the definition presented as follows:
f(x) = 3ax + 10, x ≤ -4.f(x) = bx² - 5x + 7, x > -4.The first step is to guarantee that the function is continuous, that is, that the lateral limits are equal, hence:
lim x -> -4^- f(x) = lim x -> -4^+ f(x)
lim x -> -4 3ax + 10 = lim x -> -4 bx² - 5x + 7
-12a + 10 = 16b + 27
The derivatives also have to be equal on both sides of the piece-wise function at x = -4, hence:
lim x -> -4^- f'(x) = lim x -> -4^+ f'(x)
lim x -> -4 3a = lim x -> -4 2bx - 5
3a = -8b - 5.
Then the following system of equations is built to find the values of a and b:
12a + 16b = -17.3a + 8b = -5.Multiplying the second equation by -2 and adding them, we have that the value of a is obtained as follows:
6a = -7
a = -7/6.
Then the value of b is obtained as follows:
8b = -5 - 3a
8b = -5 + 21/6
8b = -30/6 + 21/6
8b = -9/6
8b = -3/2
b = -3/16.
More can be learned about differentiable functions at https://brainly.com/question/27864122
#SPJ1
Related Questions
What is true about the relationship between variable costs and economies of scale?
Answers
Answer:
The cost per unit of fixed input decreases as output volume increases. A decrease in average variable costs (average non-fixed expenses), together with an increase in output, is another effect of economies of scale. This is caused by operational efficiency and synergies as a result of a rise in production scale.
Explanation:
For a standard normal distribution, find:
P(-1.91 < z < 0.4)
Answers
For a standard normal distribution, Probability (p) = 0.6273
A normal distribution, often known as a Gaussian distribution, is a form of the continuous probability distribution for a real-valued random variable in statistics.
A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution. The standard normal distribution is centered at zero, and the standard deviation indicates how much a specific measurement deviates from the mean.
To calculate probability, use the usual normal distribution. Because the standard normal distribution is a distribution function, the area under the curve between two points indicates the likelihood that variables will take on a range of values. The whole area under the curve is one, or one hundred percent.
Thus, for a standard normal distribution:
Using the standard normal table
P(-1.91 < z < 0.4)
= P (z<0.4) - P(z<-1.91)
= 0.6554 - 0.0281
= 0.6273
Hence,
Probability P(-1.91 < z < 0.4) under a standard normal distribution is:
P = 0.6273
Learn more about standard normal distribution:
https://brainly.com/question/13781953
#SPJ1
TOPIC
You are assigned to a walking beat downtown, and every
morning you stop into a breakfast shop and have a cup of
coffee only. The owner does not charge you. After some
citizen complaints about the parking situation in the area,
the station has directed you to ticket all illegally parked
cars. As you are tagging the cars in front of the breakfast
shop, the owner comes out furious and asks what are you
doing? He states rather loudly, "I give you free coffee every
day and this is how you repay me"?
• How would you respond?
•
• Was there an implied consent that the free coffee
would be reimbursed by granting favors to the owner?
On a larger scale, could this lead to a perception of
corruption of the officer looked the other way or
warned customers that if they were parked illegally
and didn't move their cars they would be ticketed?
What would be a solution to this issue?
Answers
Answer:
In this case, I would respond by saying that giving free breakfast can be considered as a generous effort by the shop owner but it can never mean an implied consent for grant of favors. Moreover, this could very well be perceived as corruption by the officers as they leave people without tickets despite illegally parking the vehicles and the grant of favors like the shop owner would also amount to bribery and corruption.
Explanation:
Moreover, this could very well be perceived as corruption by the officers as they leave people without tickets despite illegally parking the vehicles and the grant of favors like the shop owner would also amount to bribery and corruption.
A viable solution to issue would be to make a rule to post proper advertisements about the penalty for illegal parking should be done. These advertisements would act as awareness as well as warning for people and then officers don't need to be lenient on people who still break the rules. This way, the issue of corruption allegations and illegal parking both can be resolved together.
To know more about Corruption:
https://brainly.com/question/15270178
#SPJ1
PLEASE HELP FAST!!!!!
10.In the context of the passage as a whole, the quotes in the penultimate paragraph (lines 67–68) primarily serve to
A. suggest that the author’s argument is the prevailing opinion on the topic of millennials
B. point out a weakness in the author’s argument by illustrating a flaw in the millennial point of view
C.contrast the author’s argument with the cautionary advice offered in the conclusion
Answers
In the context of the passage as a whole, the quotes in the penultimate paragraph (lines 67–68) primarily serve to " contrast the author’s argument with the cautionary advice offered in the conclusion" (Option C)
Why does the above-named paragraph create a contrast to the advice given in the conclusion?The penultimate paragraph (that is the paragraph before the last one) suggests that the Millenials are very optimistic in a dogged way. Put in context, he already explained that much of their optimism may be driven by the wrong reason which is to show off on social media.
Note as well that he also indicates that most of them believe that their best days are ahead.
Hence, in contrast to the feeling of optimizing which most Millenials inculcate, he states that they should note that in the future that they are so optimistic about, there will be less-than-perfect days.
Learn more about context:
https://brainly.com/question/10943525
#SPJ1
Béla IV’s statement in the fourth paragraph that the Hungarian people “cannot cease to be amazed” by the actions of the papacy most directly refers to the papacy’s failure to aid the Hungarians while - initiating European military campaigns in the Middle East
Answers
Béla IV's statement in the fourth paragraph that the Hungarian people "cannot cease to be amazed" by the actions of the papacy most directly refers to the papacy's failure to aid the Hungarians while initiating European military campaigns in the Middle East is a true statement.
How did Hungary defeat Mongols?
The invasion was easily resisted, and the Mongols' invasion force was significantly reduced as a result of two significant military defeats, numerous lesser attacks, and several months of hunger. This was largely made possible by the military reforms and the new fortification network.
During the Mongol invasion of Europe, the Battle of Mohi (11 April 1241) served as the key conflict between the Mongol Empire and the Kingdom of Hungary. In Muhi (formerly Mohi), southwest of the Sajó River, it happened.
Note that between 1235 and 1270, Béla IV reigned as King of Hungary, Duke of Styria, and King of Croatia. King Andrew II's eldest son was crowned in 1214 on the initiative of a group of powerful noblemen during the reign of his father.
Learn more about Hungary from
https://brainly.com/question/12373511
#SPJ1
See full question below
Béla IV's statement in the fourth paragraph that the Hungarian people "cannot cease to be amazed" by the actions of the papacy most directly refers to the papacy's failure to aid the Hungarians while initiating European military campaigns in the Middle East. true or false.
Please help me solve with steps
Answers
The capital on 31 January 2020 was approx $ 50000 as the owner has not make any drawing this year. Hence option B is correct
What is capital?Capital is defined as the total amount of financial resources needed to manufacture goods or services. These cash may be employed to start up operations, cover ongoing costs, or develop and extend the company.
As given profit made this year = $ 10000
So the capital on 31 January 2020 = approx $ 50000
Thus, the capital on 31 January 2020 was approx $ 50000 as the owner has not make any drawing this year. Hence option B is correct
To learn more about capital, refer to the link below:
https://brainly.com/question/29052534
#SPJ1
HELP PLEASE ANSWER
1. Assume that cellular telephone manufacturers are earning short-run economic profits. Draw a correctly labeled graph for a typical firm in the industry and show each of the following.
- a. The profit-maximizing output and price
- b. The area representing economic profit
2. At the profit-maximizing price you identified in part (a), would the typical firm’s demand curve be price inelastic? Explain.
3. Given the information in part (a), what happens to the demand curve for the typical firm in the long run? Explain.
4. Using a new correctly labeled graph, show the profit-maximizing output and price for the typical firm in the long run.
5. Does the typical firm produce an output level that minimizes its average total cost in the long run?
6. In long-run equilibrium, does the typical firm produce the allocatively efficient level of output? Explain.
Answers
The above prompt is about a firm in a Monopolitically Competitive market.
What is a Monopolistically Competitive Market?When several firms offer alternative products or services that are similar but not perfect alternatives, monopolistic competition develops. In a monopolistic competitive industry, the barriers to entry are low, and the choices of any one business have little direct impact on its competitors.
Assuming that cellular telephone manufacturers in monopolistic competition are earning short-run economic profits, the correctly labeled graph for a typical firm in the industry shows each of the following:
The profit-maximizing output and priceThe area representing economic profit, are attached accordingly.2) At the profit-maximizing price you identified in part (a), the typical firm’s demand curve would NOT be price inelastic. This is because at the profit-maximizing price, the average firm's demand curve would be elastic as marginal revenue is positive in this region of the demand curve, therefore total revenue grows as price falls.
3) Given the information in part (a), what happens to the demand curve for the typical firm, in the long run, is that, If a monopolistically competitive business earns an economic profit, the demand curve for the normal firm will move to the left (or down) in the long run as new firms enter the sector to capitalize on these short-term profits. These new competitors eat into the old firm's market share, reducing demand for its product.
4) For the graph showing the profit Maximizing output and price for a typical firm in the long run, see the attached.
5) No, the typical firm does not produce an output level that minimizes its average total cost in the long run.
6) No, in long-run equilibrium, the typical firm does not produce the allocatively efficient level of output. The reason is that price for this firm in the long run is greater than it's marginal cost.
Learn more about Monopolistic Competition:
https://brainly.com/question/29407851
#SPJ1
Please Hurry due by 11 o clock tonight!!!! In picture composition, what effect offers a depth of perspective, leads the viewer to notice subject contrasts, and plays up distance, making the spatial relationship more obvious?
A. overlapping
B. monopods
C. contrasting
D. radial composition
Answers
The effect that offers a depth of perspective, leads the viewer to notice subject contrasts, and plays up distance, making the spatial relationship more obvious is A. overlapping.
What is overlapping?When shapes overlap, they are in front of other shapes. When one shape overlaps another, it creates the illusion of depth.
The effect provides depth of perspective, draws attention to subject contrasts, and emphasizes distance, making the spatial relationship more obvious.
In art, overlapping is the placement of objects over one another to create the illusion of depth. An example is painting is a two-dimensional form of art. It is long and wide but has no depth.
Learn more about art on:
https://brainly.com/question/1504175
#SPJ1