Maxima And Minima
Muhtasari
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.
Malengo
- Apply differentiation to practical problems involving maxima and minima.
- Use the first and second derivative tests to distinguish between maxima and minima.
Somo la Sauti
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Ramani ya mawazo
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Maelezo ya Somo
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Tathmini ya Somo
Hongera kwa kukamilisha somo la Maxima And Minima. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.
Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.
Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.
- 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
Fanyia kazi maswali haya kwenye programu
Fanyia kazi maswali haya kwenye programu
Vitabu Vinavyopendekezwa
Fanya Mazoezi ya Maswali ya Majaribio
Ungependa kufanya mazoezi ya maswali ya majaribio kuhusu Maxima And Minima? Pakua programu ya Green Bridge CBT ili kupata maswali ya majaribio na tathmini kamili za mazoezi kuhusu mada hii.
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Kila kitu unachohitaji ili kufaulu katika JAMB, WAEC & NECO.
