Cho hàm số \(f(x)\) là hàm đa thức bậc 3 và có đồ thị như hình vẽ.
Xét hàm số \(g(x)=f\left(2 x^{3}+x-1\right)+m\). Với giá trị nào của \(m\) thì giá trị nhỏ nhất của \(g(x)\) trên đoạn \([0;1]\) bằng \(- 20\).
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Đặt \(u=2 x^{3}+x-1 \Rightarrow u^{\prime}=6 x^{2}+1>0\) với \(\forall x\)
\(\Rightarrow x \in[0 ; 1] \Leftrightarrow u \in[-1 ; 2]\)
Xét \(g(x)=f(u)+m\) với \(u \in[-1 ; 2] \Rightarrow g^{\prime}(x)=u^{\prime}. f^{\prime}(u)\)
\(\Rightarrow g^{\prime}(x)=0 \Leftrightarrow u^{\prime}. f^{\prime}(u)=0 \Leftrightarrow f^{\prime}(u)=0 \Leftrightarrow u= \pm 1\)
BBT
\(\Rightarrow \min _{[0 ; 1]} g(x)=-20 \Leftrightarrow-1+m=-20 \Leftrightarrow m=-19\).
Câu hỏi liên quan
Read the following advertisement and mark the letter A, B, C, or D on your answer sheet to indicate the option that best fits each of the numbered blanks from 1 to 6.
Fire Ant Festival 2024 - November 25
The upcoming Fire Ant Festival will be an incredibly exciting event, where you will be introduced (1)______ lively games and thrilling activities. In a vibrantly decorated outdoor space, visitors will have the chance to take part in traditional games such as tug-of-war, endurance competitions, and on-land boat racing. The highlight of the festival is the (2)______, where teams will compete to create (3)______ fire ant-inspired structures. Additionally, guests can enjoy breathtaking fire dance performances (4)______ by professional artists from various regions. Although named after a creature known to(5)______ a threat to many other species, the festival has proven to be safe for visitors. The festival is also an opportunity for visitors to try unique traditional folk games, which have been preserved and developed over many generations. Come join us to soak up the lively atmosphere, we promise(6)____ you unforgettable memories!
Which of the following situation best exemplifies “trade-in”?
Chiến thằng Cầu Giấy lần thứ hai của nhân dân ta (1883) là sự kết hợp chiến đấu giữa đội quân của
Thị trường ra đời từ khi nào sau đây?
Cho các tập hợp $G=\{x \in \mathbb{R} \mid-12 \leq x \leq 21\} ; H=\{x \in \mathbb{R} \mid 0 \leq x \leq 17\}$
a) \(G = \left[ { - 12\,;\,21} \right]\).
b) \(H = \left[ {0;17} \right]\).
c) \(G \subset H\).
d) \(H \subset G\).
Sự di cư theo mùa của một số loài chim thường được biểu hiện bằng phương pháp gì?
Độ dịch chuyển là một đại lượng:
CHỦ ĐỀ: GIẢI NOBEL HÓA HỌC 2020
(Tham khảo bài văn của chủ đề trong đường link dưới đây ở trang 21)
https://tvsthpt.dlib.vn/app/doc-sach-ebook/d00ddd794efd
Và trả lời câu hỏi sau:
Theo đoạn [4] và [5], có thể điều trị khỏi các bệnh di truyền do đột biến gen khi áp dụng công cụ CRISPR/Cas9 để tăng cường hệ miễn dịch của vi khuẩn nhằm kháng lại virus tấn công từ bên ngoài.
Đúng hay sai?
Việc Rơn-ghen phát hiện ra tia X có ý nghĩa gì quan trọng?
Tập hợp nào sau đây có đúng một tập hợp con?
Nhận định nào dưới đây là bàn về đặc điểm hoạt động của Hội đồng nhân dân?
Read the passage below and choose A, B, C or D to answer each question from 636 - 640.
Many of the most damaging and life-threating types of weather-torrential rains, severe thunderstorms, and tornadoes-begin quickly, strike suddenly, and dissipate rapidly, devastating small regions while leaving neighboring areas untouched. One such event, a tornado, struck the northeastern section of Edmonton, Alberta, in July 1987. Total damages from the tornado exceeded $250 million, the highest ever for any Canadian storm. Conventional computer models of the atmosphere have limited value in predicting short-live local storms like the Edmonton tornado, because the available weather data are generally not detailed enough to allow computers to discern the subtle atmospheric changes that precede these storms. In most nations, for example, weather balloon observations are taken just once every twelve hours at locations typically separated by hundreds of miles. With such limited data, conventional forecasting models do a much better job predicting general weather conditions over large regions than they do forecasting specific local events.
Until recently, the observation-intensive approach needed for accurate, very short range forecasts, or “Nowcasts”, was not feasible. The cost of equipping and operating many thousands of conventional weather stations was prohibitively high, and the difficulties involved in rapidly collecting and processing the raw weather data from such a network were insurmountable. Fortunately, scientific and technological advances have overcome most of these problems. Radar systems, automated weather instruments, and satellites are all capable of making detailed, nearly continuous observation over large regions at a relatively low cost. Communications satellites can transmit data around the world cheaply and instantaneously, and modern computers can quickly compile and analyzing this large volume of weather information. Meteorologists and computer scientists now work together to design computer programs and video equipment capable of transforming raw weather data into words, symbols, and vivid graphic displays that forecasters can interpret easily and quickly. As meteorologists have begun using these new technologies in weather forecasting offices, Nowcasting is becoming a reality.
What does the passage mainly discuss?
Trong sinh sản sinh dưỡng ở thực vật, cây mới được tạo ra như thế nào?
Phần mềm trình chiếu (Microsoft Power Point) là?
Read the following passage about The Elderly in Multicultural Societies: Challenges and Opportunities 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 23 to 30.
In multicultural societies, elderly individuals face unique challenges and important opportunities. As communities diversify rapidly, traditional support systems are constantly evolving. Seniors often navigate unfamiliar cultural environments while facing significant language barriers that lead to social isolation. These persistent obstacles frequently prevent full access to essential healthcare services or meaningful community participation. Fortunately, innovative local organizations address these critical issues by offering comprehensive translation services and culturally sensitive care options.
Technology presents both remarkable benefits and considerable difficulties for elderly individuals from various cultural backgrounds. Digital tools effectively connect seniors with distant family members globally, yet many older adults struggle substantially with these new communication methods. Recent research shows approximately 65% of elderly immigrants experience digital exclusion compared to native-born seniors. In response, numerous community centers have successfully established specialized technology workshops for older adults from diverse backgrounds, helping them maintain vital connections with overseas relatives and friends.
Cultural differences significantly impact elderly care approaches across communities. In collectivist cultures, elderly family members traditionally live with their children, while Western societies typically emphasize personal independence. This fundamental divergence creates tension when immigrant families attempt to adapt to new societal norms. However, vibrant multicultural environments provide valuable opportunities for exchanging diverse perspectives on aging. Many communities benefit tremendously from adopting hybrid approaches blending traditional cultural practices with modern care techniques, creating more comprehensive support systems.
Economic aspects of aging in multicultural contexts matter significantly for overall wellbeing. Elderly immigrants frequently face severe financial hardships due to limited retirement savings and persistent employment discrimination throughout their lives. Some progressive governments implement supportive policies addressing these vulnerable individuals' unique needs. Certain forward-thinking regions offer specialized employment programs for seniors with diverse cultural backgrounds, recognizing their valuable skills and extensive life experiences. Additionally, creative intergenerational initiatives connecting elderly immigrants with younger community members effectively foster mutual understanding and practical support, successfully transforming demographic challenges into meaningful community enrichment opportunities.
The word “divergence” in paragraph 3 could be best replaced by _________.
Quyền và nghĩa vụ trong việc thực hiện quy định của pháp luật về ngân sách nhà nước được thể hiện qua ý nào dưới đây?
Một ô tô bắt đầu chuyển động thẳng nhanh dần đều từ trạng thái đứng yên. Trong 4 s đầu ô tô đi được đoạn đường 10 m và không đổi chiều chuyển động. Tính vận tốc của ô tô ở cuối giây thứ hai.
Ngày nào ở bán cầu Nam có thời gian ban ngày dài nhất, thời gian ban đêm ngắn nhất trong năm?
Vectơ nào dưới đây là một vectơ chỉ phương của đường thẳng song song với trục \(Ox?\)
In the writer's opinion, ____.