Cho hàm số \(f(x)=x^{3}-m x^{2}-m^{2} x+8(*)\), với \(m\) là tham số thực.
Cho hàm số \(y=x^{3}-m x^{2}-m^{2} x+8\). Có bao nhiêu giá trị \(m\) nguyên đề hàm số có điểm cực tiểu nằm hoàn toàn phía trên trục hoành?
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Ta có: \(y^{\prime}=3 x^{2}-2 m x-m^{2}, y^{\prime}=0 \Leftrightarrow\left[\begin{array}{l}x=m \\ x=-\frac{m}{3}\end{array}\right.\).
Để hàm số có hai điểm cực trị thì \(y^{\prime}=0\) có hai nghiệm phân biệt \(\Leftrightarrow m \neq 0\).
Trường hợp 1: \(m>0 \Rightarrow y_{c t}=y(m)=-m^{3}+8>0 \Leftrightarrow m<2\).
Vậy \(0<m<2 \Rightarrow\) có 1 giá trị nguyên \(m=1\).
Trường hợp 2: \(m<0 \Rightarrow y_{c t}=y\left(-\frac{m}{3}\right)=\frac{5}{27} m^{3}+8>0 \Leftrightarrow m>-\frac{6}{\sqrt[3]{5}}\).
Vậy \(-\frac{6}{\sqrt[3]{5}}<m<0 \Rightarrow\) có 3 giá trị nguyên của \(m\) là \(\{-3 ;-2 ;-1\}\).
Vậy tổng số có 4 giá trị nguyên của \(m\).
Câu hỏi liên quan
Có bao nhiêu cặp số nguyên \((x, y)\) thỏa mãn điều kiện \(0 \leq y \leq 100\) và \(x^{6}+6 x^{4} y+12 x^{2} y^{2}-19 y^{3}+3 x^{2}-3 y=0 ?\)
"Nhà nước bảo đảm thực hiện chính sách đối với người có công, có chính sách trợ giúp người cao tuổi, người khuyết tật" là đang thể hiện nội dung của Hiến pháp năm 2013 trên lĩnh vực nào?
Nội dung nào dưới đây thể hiện quyền học tập của công dân?
Read the following passage about lifelong learning and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
My father was an enthusiastic traveller, but as he got older, he increasingly suffered from what he called “travel fever,” a vivid term for the acute anxiety felt before a journey, essentially due to uncertainty about all the things that could go wrong. Sadly, this eventually stopped him from going on holiday. Then I, too, started to suffer similar apprehension, so I consulted a psychotherapist. She recommended a small piece of cognitive behavioural therapy, which involved acknowledging the mental and physical symptoms of anxiety, but telling myself that these were essentially indistinguishable from feelings of excitement about the prospect of a journey. This reframing of my feelings has been reasonably effective – it’s one way of dealing with uncertainty.
It’s not just the uncertainty of travel that we all have to face. None of us knows what is going to happen, or what is currently going on outside our immediate knowledge, or the vast majority of what has happened in the past. Uncertainty has been called the “conscious awareness of ignorance,” and there is a lot we are ignorant about. We must navigate through life without complete information, and this fundamental uncertainty is an inescapable aspect of human existence.
We all have to live with this uncertainty and, as a statistician, it’s been my job to try to analyse data and assess some of the risks we face. (I)But some deal with uncertainty with more equanimity than others. (II) Psychological studies, as well as our own experience, reveal a wide variation in people’s responses, including those that are cognitive (how we think), emotional (how we feel), and behavioural (what we do). (III)For example, when faced with uncertainty, do you deny it or acknowledge it, does it put the wind up you or make you courageous, do you try to avoid it or approach it?(IV)
Of course, your response may depend on the context, just as an individual’s appetite for risk-taking can vary across different areas of their lives. I have known people who seemed to take huge physical risks, yet were very cautious with money. Numerous scales have been developed to measure how well people can deal with uncertainty, based on responses to statements ranging from “Unforeseen events upset me greatly” to “When it’s time to act, uncertainty paralyses me.” Those who score highly, and find it difficult to tolerate uncertainty, may also be at increased risk of clinically significant anxiety and depression.
Which of the following best summarizes paragraph 4?
Cho 40 tấm thẻ được đánh số từ 1 đến 40, chọn ngẫu nhiên 3 tấm thẻ. Tính xác suất để chọn được 3 tấm thẻ có tổng các số ghi trên các thẻ là một số chẵn.
Phần tô màu (không bao gồm đường thẳng \(d\)) trong hình vẽ là miền nghiệm của bất phương trình nào sau đây?
"Nếu Tổ quốc neo mình đầu sóng cả
Những chàng trai ra đảo đã quên mình
Một sắc chỉ về Hoàng Sa thuở trước
Còn truyền đời con cháu mãi đinh ninh
Nếu Tổ quốc nhìn từ bao mất mát
Máu xương kia dằng dặc suốt ngàn đời
Hồn dân tộc ngàn năm không chịu khuất
Dáng con tàu vẫn hướng mãi ra khơi"
(Trích Tổ quốc nhìn từ biển - Nguyễn Việt Chiến)
Phong cách ngôn ngữ nào được sử dụng trong đoạn trích trên?
Nguyen Thi Anh Vien performed so well at the 28th Sea Games Women’s 200m butterfly that none of her rivals could __________ her.
Một lực có độ lớn 3 N tác dụng vào một vật có khối lượng 1,5 kg lúc đầu đứng yên. Xác định quãng đường mà vật đi được trong khoảng thời gian 2 s.
Read the following passage about studying abroad and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Successful students often do the followings while studying. First, they have an overview before reading. Next, they look for important information and pay greater attention to it (which often needs jumping forward or backward to process information). They also relate important points to one another. Also, they activate and use their prior knowledge. When they realize that their understanding is not good, they do not wait to change strategies. Last, they can monitor understanding and take action to correct or “fix up” mistakes in comprehension.
Conversely, students with low academic achievement often demonstrate ineffective study skills. [I] They tend to assume a passive role in learning and rely on others (e.g., teachers, parents) to monitor their studying. [II] For example, low-achieving students often do not monitor their understanding of content; they may not be aware of the purpose of studying; and they show little evidence of looking back or employing “fix-up” strategies to fix understanding problems. [III] Students who struggle with learning new information seem to be unaware that they must extend effort beyond simply reading the content to understand and remember it. [IV]
Children with learning disabilities do not plan and judge the quality of their studying. Their studying may be disorganized. Students with learning problems face challenges with personal organization as well. They often have difficulty keeping track of materials and assignments, following directions, and completing work on time. Unlike good studiers who employ a variety of study skills in a flexible yet purposeful manner, low-achieving students use a restricted range of study skills. They cannot explain why good study strategies are important for learning; and they tend to use the same, often ineffective study approach for all learning tasks, ignoring task content, structure or difficulty.
The word ‘They’ in the 1st paragraph refers to ______
Công ty X chuyên sản xuất về bánh bao, trong quá trình tạo ra thành phẩm, nhà sản xuất đã chia các yếu tố như nhân bánh, vỏ bánh và hộp bánh cho các đơn vị sản xuất khác nhau. Trong trường hợp trên, nhà sản xuất đã thực hiện hoạt động gì của kinh tế?
Mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the following questions.
There ______ something vaguely familiar about her face but I couldn't remember where I______her before.
Thị trường bao gồm những yếu tố cơ bản nào?
To participate in the competition, all participants must ________ to the safety guidelines provided by the organizers.
Nguyên lí của thí nghiệm hô hấp ở hạt nảy mầm là gì?
Phản ứng nào dưới đây không thể hiện tính oxi hóa - khử của hợp chất aldehyde?
Một loại tế bào bạch cầu tổng hợp protein xuất ra khỏi tế bào. Phân tử protein đã được vận chuyển qua các bào quan theo trật tự nào sau đây?
Cho S.ABCD có đáy là hình bình hành. Gọi M, N, Q lần lượt là trung điểm của BC, CD và SA. Thiết diện của mp(MNQ) với hình chóp là:
Read the following passage about urban shift and mark the letter A, B, C, D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
[I] Sperm whales are fascinating creatures. [II] They possess the biggest brain of any species, six times larger than a human’s, which scientists believe may have evolved to support intelligent, rational behavior. [III] They’re also highly social and capable of making decisions as a group. [IV] But there’s also a lot we don’t know about them, including what they may be saying to one another when communicating with a system of short clicks, known as codas.
Now, new research published in Nature Communications today suggests that sperm whales’ communication is actually much more expressive and complicated than was previously thought. A team of researchers led by Pratyusha Sharma at MIT’s Computer Science and Artificial Intelligence Lab (CSAIL) working with Project CETI, a nonprofit focused on using AI to understand whales, used statistical models to analyze whale codas and managed to identify a structure to their language that’s similar to features of human language. Their findings represent a tool future researchers could use to decipher not just the structure but the actual meaning of whale sounds.
For the study, the researchers examined recordings of 8,719 codas from around 60 whales collected by the Dominica Sperm Whale Project between 2005 and 2018, using a mix of AI algorithms for pattern recognition and classification. The AI then turned the clicks within the coda data into a new kind of data visualization called an exchange plot, revealing that some codas featured extra clicks. These extra clicks, combined with variations in the duration of their calls, appeared in interactions between multiple whales, which they say suggests that codas can carry more information and possess a more complicated internal structure than we had previously believed.
The team’s next step is to build language models of whale calls and to examine how those calls relate to different behaviors. They also plan to work on a more universal system that could be used across species, says Sharma. Taking a communication system we know nothing about, working out how it encodes and transmits information, and slowly beginning to understand what’s being communicated could have many purposes beyond whales. “I think we’re just starting to understand some of these things,” she says. “We’re very much at the beginning, but we are slowly making our way through.”
Which of the following can most likely be inferred from the passage?
Which of the following best restates each of the given sentence?
Perhaps I saw Linda dating with your ex-boyfriend at Roses Restaurant last night.