Maxima And Minima
Bayani Gaba-gaba
Differentiation finds the high and low points of a curve: where it stops rising and starts falling, or the reverse. This is the key to optimisation, finding the greatest area, the least cost, the maximum height.
In this lesson you will apply differentiation to find stationary points and to practical maxima and minima problems, using the first and second derivative tests to tell a maximum from a minimum.
Manufura
- Apply differentiation to practical problems involving maxima and minima.
- Use the first and second derivative tests to distinguish between maxima and minima.
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Katunan tunawa
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Nazarin Darasi
Barka da kammala darasi akan Maxima And Minima. Yanzu da kuka bincika mahimman raayoyi da raayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.
Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.
Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.
- At a stationary point, dy/dx equals: A. 1 B. 0 C. the y-value D. infinity Answer: B
- For y = x^3 - 3x, the stationary points are at x =: A. 0 only B. ±1 C. ±3 D. 1 and 3 Answer: B
- If d^2y/dx^2 < 0 at a stationary point, it is a: A. minimum B. maximum C. point of inflexion D. root Answer: B
- If d^2y/dx^2 > 0 at a stationary point, it is a: A. maximum B. minimum C. root D. asymptote Answer: B
- For y = x^3 - 3x, the local maximum is at: A. (-1, 2) B. (1, -2) C. (0, 0) D. (1, 2) Answer: A
Yi aikin wadannan tambayoyi a cikin manhaja
Yi aikin wadannan tambayoyi a cikin manhaja
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