1. 2.2 Geometrical Application of Calculus
Types of Stationary Points
1. Minimum - + - + - + - + - + - - + + x
LHS
Minimum
RHS
f’(x)
< 0
= 0
> 0

2. 2.2 Geometrical Application of Calculus
Types of Stationary Points
2. Maximum - + - + - + - - + - + x
LHS
Maximum
RHS
f’(x)
> 0
= 0
< 0

3. 2.2 Geometrical Application of Calculus
Types of Stationary Points - +
3.Point of
Horizontal
Inflection - + - + - - + - + - + - - + - + - x
LHS
Inflection
RHS
f’(x)
> 0
< 0

4. 2.2 Geometrical Application of Calculus
Types of Stationary Points
Find any stationary points on the curve
f(x) = x2 - 2x & determine what type it is.
f’(x) = 2x - 2
f(1) = (1)2 – 2(1) = -1
2x - 2 = 0 (Stationary)
(1, -1)
2x = 2
f’(0) = 2(0) - 2 = -2
x = 1
f’(2) = 2(2) - 2 = +2
LHS x = 0
Stationary x = 1
RHS x = 2 - +
(1, -1) is a Minimum

5. (0, 2) is a horizontal point of inflection
2.2 Geometrical Application of Calculus
Types of Stationary Points
2. Find the turning point on the curve
y = 2x3 + 2 and determine what type it is.
f(x) = 2x3 + 2
f(0) = 2(0)3 + 2 = 2
f’(x) = 6x2
(0, 2)
f’(-1) = 6(-1)2 = +6
6x2 = 0 (Stationary)
x = 0
f’(1) = 6(1)2 = +6
LHS x = -1
Stationary x = 0
RHS x = 1 +
(0, 2) is a horizontal point of inflection