5. (10%) Find the tangent line of x^4 - x^2y + 2xy^4 = 4 passing through (1,1).

四、請閱讀以下研究報告之結論，並請詳述其意涵，及評論其所述內容。(25%)In early 2020 COVID-19 ravaged many countries around the world. Everyday life in many cities have been interrupted ever since. As many parts of the world continue to struggle with the COVID-19 pandemic, the scientific community has made efforts to shed more light on its underlying dynamics. Drawing on the early evidence reported in the literature, in this study, we tried to understand major impacts on various urban sectors, identify key factors that should be considered for better preparation and response to future similar events, and high-light gaps that need to be further studied in the future research.This review shows that early evidence is mainly related to four major themes, namely, (1) environmental quality, (2) socio-economic impacts, (3) management and governance, and (4) transportation and urban design. However, there is no balanced coverage of these themes, and issues related to the first theme are dominant. This is probably because data related to air quality and environmental impacts is more readily available, but accessing and analyzing data related to other themes may need more time.While some common patterns can be observed, existing evidence indicates that impacts and response mechanisms differ from one context to another, and it is not always easy to provide identical recommendations that apply to different cities. However, like any other crisis, COVID-19 provides lessons that can be used to build back better. Major issues revealed by the pandemic and possible lessons/ recommendations for better planning in the post-COVID era are presented in this article. It provides some insights into how to handle the present and any future similar events that occur in cities.Clearly, cities need to re-evaluate their policies in different sectors. For instance, improvements in air and water quality during lockdown periods once again highlight the significant environmental impacts of anthropogenic activities and provide a wake-up call to adopt environmentally friendly development pathways. The pandemic has also exposed old socioeconomic inequalities that exist in cities. It was discussed how such inequalities could threaten public health by making it difficult to enforce protective measures such as social distancing. Obviously, overcoming such inequalities is critical and should be prioritized as cities recover from the pandemic.The pandemic is expected to fundamentally alter how cities are managed/governed in the future. In this regard, actions taken within the next few years are important and determine whether post-COVID cities will be developed and managed in a more sustainable manner. As cities start to recover, their main priority will probably be economic development. However, it is essential to make sure that, in addition to economic development, social and environmental dimensions of sustainability will also be considered. In fact, the pandemic has provided opportunities that can be capitalized on by planners. For instance, in the transportation section, it was discussed that public transportation has been severely affected during the pandemic, and many people have turned to private vehicles and biking/walking as safer alternatives. While increased interest in private vehicles poses threats to achieving sustainable development, the increase in the number of cyclists in many cities around the world provides a unique window of opportunity to promote cycling culture in cities further. This may turn temporary cyclists into long-term riders.

5. (10%) Find the tangent line of \( x^4 - x^2y + 2xy^4 = 4 \) passing through (1,1).

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