Title: Higher order Derivatives & Stationary point H/W Marking

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Presentation transcript:

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

Gradient of the curve at a particular point RECAP

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.

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

Question regarding Differentiation (as a rate of change measure)

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)

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.

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