1. Title: Higher order Derivatives & Stationary point H/W Marking
22/09/17
LO: TBAT learn higher order differentiation
:TBAT mark find the stationary points on a curve
Title: Higher order Derivatives & Stationary point
H/W Marking
Literacy in Maths
Derivative function
Stationary point
Maximum
Minimum
Local and Global

2. Gradient of the curve at a particular point
RECAP

4. Higher Order Derivatives
The Higher derivative or second derivative, or the second order derivative, of a function f is the derivative of the ‘derivative of f’.
It is denoted by F’’(x) or d2y/dx2
It is also called Repeat Differentiation.

6. FINDING THE RATE OF CHANGE AT A PARTICULAR POINT ON F(x)

7. Question regarding Differentiation (as a rate of change measure)

8. STATIONARY POINTS (Critical points)
POINT OF INFLECTION
(a point of a curve at which a change in the direction of curvature
occurs)
MAXIMUM
(Gradient changes from
+ve to –ve)
MINIMUM POINT
(Gradient changes from
-ve to +ve)
At the stationary points, dy/dx= 0 (since the gradient is zero at stationary points)

11. Find the coordinates of the stationary points on the graph y = x2
Find the coordinates of the stationary points on the graph y = x2 . We know that. By differentiating, we get: dy/dx = 2x. Therefore the stationary points on this graph occur when 2x = 0, which is when x = 0.

12. A point of a curve at which a change in the direction of curvature occurs is called point of inflection (or point of inflexion)