A' sgeidseadh lùb
Gus lùb fuincsean a sgeidseadh, feumaidh tu:
- Am fuincsean a dhiofarachadh
- Suidhich \(\frac{{dy}}{{dx}} = 0\)
- Cuir abairt ann an camagan. Mar eisimpleir, 18x + 12y = 6(3x + 2y). 'S e factaradh am pròiseas meudachaidh a' dol an rathad eile. agus an uair sin fuasgail gus an obraich thu a-mach na co-chomharran-\(x\) aig na puingean suidhichte
- Obraich a-mach nàdar na lùib a' cleachdadh nan co-chomharran-\(x\) ann an clàr nàdair gus cumadh na lùib a dhearbhadh air taobh clì agus deas nam puingean suidhichte
- Ionadaich a-steach na co-chomharran-\(x\) aig puingean suidhichte dhan cho-aontar thùsail aig an lùib agus obraich a-mach na co-chomharran-\(y\) aig na puingean sin
- Obraich a-mach càit a bheil an lùb a' gearradh a' \(y\)-axis le bhith ag ionadachadh \(x = 0\) a-steach do cho-aontar tùsail na lùib
- Obraich a-mach càit a bheil an lùb a' gearradh an \(x\)-axis le bhith ag ionadachadh \(y = 0\) a-steach do cho-aontar tùsail na lùib
- Sgeids an lùb
Eisimpleir
Sgeids an lùb \(y = {x^2} + 4x - 5\)
Fuasgladh
\(\frac{{dy}}{{dx}} = 2x + 4\)
Bidh puingean suidhichte ann nuair a tha \(\frac{{dy}}{{dx}} = 0\)
\(2x + 4 = 0\)
\(2(x + 2) = 0\)
\(x + 2 = 0\)
\(x = - 2\)
\(\frac{{dy}}{{dx}} = 2( - 3) + 4 = - 6 + 4 = - 2\) (àicheil)
\(\frac{{dy}}{{dx}} = 2( - 2) + 4 = - 4 + 4 = 0\) (suidhichte)
\(\frac{{dy}}{{dx}} = 2( - 1) + 4 = - 2 + 4 = 2\) (dearbhte)
Co-chomharran-y
Nuair a tha \(x = - 2\)
\(y = {x^2} + 4x - 5\)
\(y = {( - 2)^2} + 4( - 2) - 5\)
\(= 4 - 8 - 5 = - 9\)
Mar sin tha a' phuing-tionndaidh as lugha aig \(( - 2, - 9)\)
A' gearradh a' y-axis nuair a tha \(x = 0\)
\(y = {x^2} + 4x - 5\)
\(y = {0^2} + 4(0) - 5 = - 5\)
Mar sin a' gearradh a' \(y\)-axis aig \((0, - 5)\)
A' gearradh an \(x\)-axis nuair a tha \(y = 0\)
\(y = {x^2} + 4x - 5\)
\({x^2} + 4x - 5 = 0\)
\((x + 5)(x - 1) = 0\)
\(x + 5 = 0\)
\(x = - 5\)
no
\(x - 1 = 0\)
\(x = 1\)
Mar sin a' gearradh an \(x\)-axis aig \((-5, 0)\) agus \((1, 0)\)
Question
Sgeids an lùb \(y = {x^3} + 3{x^2}\)
\(\frac{{dy}}{{dx}} = 3{x^2} + 6x\)
Bidh puingean suidhichte ann nuair a tha \(\frac{{dy}}{{dx}} = 0\).
\(3{x^2} + 6x = 0\)
\(3x(x + 2) = 0\)
\(3x = 0\)
\(x = 0\)
no
\(x + 2 = 0\)
\(x = -2\)
\(\frac{{dy}}{{dx}} = 3{( - 3)^2} + 6( - 3) = 27 - 18 = 9\) (dearbhte)
\(\frac{{dy}}{{dx}} = 3{( - 2)^2} + 6( - 2) = 12 - 12 = 0\) (suidhichte)
\(\frac{{dy}}{{dx}} = 3{( - 1)^2} + 6( - 1) = 3 - 6 = - 3\) (àicheil)
\(\frac{{dy}}{{dx}} = 3{(0)^2} + 6(0) = 0 + 0 = 0\) (suidhichte)
\(\frac{{dy}}{{dx}} = 3{(1)^2} + 6(1) = 3 + 6 = 9\) (dearbhte)
Co-chomharran-y
Nuair a tha \(x = - 2\)
\(y = {x^3} + 3{x^2}\)
\(y = {( - 2)^3} + 3{( - 2)^2} = - 8 + 12 = 4\)
Nuair a tha \(x = 0\)
\(y = {x^3} + 3{x^2}\)
\(y = {0^3} + 3{(0)^2} = 0 + 0 = 0\)
Mar sin tha a' phuing-tionndaidh as motha aig \(( - 2, 4)\) agus a' phuing-tionndadh as lugha aig \((0,0)\)
A' gearradh a' y-axis nuair a tha \(x = 0\)
\(y = {x^3} + 3{x^2}\)
\(y = {0^3} + 3{(0)^2} = 0\)
Mar sin a' gearradh a' \(y\)-axis aig \((0,0)\)
A' gearradh an \(x\)-axis nuair a tha \(y = 0\)
\(y = {x^3} + 3{x^2}\)
\({x^3} + 3{x^2} = 0\)
\({x^2}(x + 3) = 0\)
\({x^2} = 0\)
\(x = 0\)
no
\(x + 3 = 0\)
\(x = - 3\)
Mar sin a' gearradh an \(x\)-axis aig \((0, 0)\) agus \((- 3, 0)\)
