Green Bridge Learning Resource Nchekwa Maka Gradients, Tangents And Normals

Gbogbo ọrọ náà

Differentiation gives the gradient of a curve at any point, and from that single value you can write the equation of the tangent (the line that just touches the curve) and the normal (the line at right angles to it).

In this lesson you will use differentiation to find gradients, tangents and normals to a curve.

Ayẹwo Ẹkọ

Ekele diri gi maka imecha ihe karịrị na Gradients, Tangents And Normals. 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.

For y = x^2, the gradient at x = 2 is: A. 2 B. 4 C. 8 D. 1 Answer: B
The tangent to y = x^2 at (2, 4) is: A. y = 2x B. y = 4x - 4 C. y = 4x + 4 D. y = x - 2 Answer: B
If a tangent has gradient 4, the normal has gradient: A. 4 B. -4 C. 1/4 D. -1/4 Answer: D
The normal to a curve is: A. parallel to the tangent B. perpendicular to the tangent C. the same as the tangent D. horizontal Answer: B
To find the gradient at a point you: A. integrate then substitute B. differentiate then substitute C. substitute then differentiate D. only substitute Answer: B