Diese Präsentation wurde erfolgreich gemeldet.
Wir verwenden Ihre LinkedIn Profilangaben und Informationen zu Ihren Aktivitäten, um Anzeigen zu personalisieren und Ihnen relevantere Inhalte anzuzeigen. Sie können Ihre Anzeigeneinstellungen jederzeit ändern.
Nächste SlideShare
×

# Increasing decreasing functions

1.309 Aufrufe

Veröffentlicht am

Increasing/Decreasing Functions

Veröffentlicht in: Bildung
• Full Name
Comment goes here.

Are you sure you want to Yes No

• Gehören Sie zu den Ersten, denen das gefällt!

### Increasing decreasing functions

1. 1. Block 1 Increasing/Decreasing Functions
2. 2. What is to be learned? • What is meant by increasing/decreasing functions • How we work out when function is increasing/decreasing • How to show if a function is always increasing/decreasing
3. 3. increasing increasing decreasing need to find SPs dy /dx = 0 Increasing → dy /dx is +ve Decreasing → dy /dx is -ve
4. 4. Ex y = 4x3 – 3x2 + 10 Function Decreasing? For SPs dy /dx = 0 dy /dx = 12x2 – 6x 12x2 – 6x = 0 6x(2x – 1) = 0 6x = 0 or 2x – 1 = 0 x = 0 or x = ½
5. 5. Nature Table y = 4x3 – 3x2 + 10 dy /dx = 12x2 – 6x = 6x(2x – 1) SPs at x = 0 and ½ x 0 dydy //dxdx = 6x(2x – 1)= 6x(2x – 1) 0 -1 ¼ = + = - Slope Max TP at x = 0 ½ 1 = + 0 Min TP at x = ½ - X - + X - + X + Decreasing 0 < x < ½
6. 6. Function always increasing? • dy /dx always +ve (i.e > 0) Ex y =x3 + 7x dy /dx = 3x2 + 7 Increasing as dy /dx > 0 for all x.
7. 7. Function always decreasing • dy /dx always -ve (i.e < 0) Ex y = -6x -x3 dy /dx = -6 - 3x2 Decreasing as dy /dx < 0 for all x.
8. 8. Less obvious y = 1 /3x3 + 3x2 + 11x dy /dx= x2 + 6x + 11 completing square (x + 3)2 – 9 + 11 (x + 3)2 + 2 Increasing as dy /dx > 0 for all x.
9. 9. Increasing/Decreasing Functions • Increasing → Gradient +ve (dy /dx > 0) • Decreasing → Gradient -ve (dy /dx < 0) • Find SPs (only need x values) • Completing square can be handy tactic
10. 10. Ex y = 1 /3x3 + 4x2 + 17x dy /dx= x2 + 8x + 17 completing square (x + 4)2 – 16 + 17 (x + 4)2 + 1 Increasing as dy /dx > 0 for all x.