12. differentiation Flashcards
1
Q
if y = ax^n dy/dx=
A
anx^n-1
2
Q
how to know if its an increasing function
A
f’(x) > 0
3
Q
how to know if its a decreasing function
A
f’(x) < 0
4
Q
3 types of stationary points
A
local maximum
point of inflection
local minimum
5
Q
max point
f’(x -b)
f(x)
f’(x+b)
A
pos
0
neg
6
Q
min point
f’(x -b)
f(x)
f’(x+b)
A
neg
0
pos
7
Q
point of infection
f’(x -b)
f(x)
f’(x+b)
A
neg 0 neg
pos 0 pos
8
Q
f’‘(a) > 0
A
min
9
Q
f’‘(a) < 0
A
max
10
Q
f’‘(a) = 0
A
y
11
Q
max min
A
cuts the x axis
12
Q
point of inflection
A
touches the x axis
13
Q
pos gradient
A
above x axis
14
Q
neg gradient
A
below x axis
15
Q
when f(x) is concave
A
the rate of change of the gradient is decreasing
16
Q
f(x) is convex
A
the rate of change of the gradient is increasing
