Green Bridge Learning Resource Nchekwa Maka Maxima And Minima

Gbogbo ọrọ náà

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.

Ayẹwo Ẹkọ

Ekele diri gi maka imecha ihe karịrị na Maxima And Minima. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.

Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.

Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.

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