Curve Sketching Flashcards
0
Q
How to find possible points of inflexion
A
F”(x) = 0
1
Q
How to find stationary points
A
F’(x) = 0
To determine nature
F”(point on either side) > 0, minimum
F”(point on either side) < 0, maximum
2
Q
How to find intercepts
A
X - y = 0
Y - x = 0
3
Q
How to find symmetry
A
Odd or even function.
4
Q
How to find asymptotes
A
Lim
x➡️infinity
x➡️-infinity
5
Q
Maximum and minimum problems - what to do
A
- Diagram
- Equations.
- Eliminate a variable.
- Differentiate
- Nature of stationary point.
* SA and volume formulas.
6
Q
SA formulas
A
B
7
Q
Volume formulas
A
B
8
Q
Growth and decay
A
P = Ae^kt
DP/Dt = kAe^kt
9
Q
Harder growth and decay
A
P = B - Ae^kt. ➡️ P - B = -Ae^kt
DP/Dt = -K(P - B)
