Graphs 10 y 5 x -6 -4 -2 2 4 6 © Annie Patton Next Slide

Aim of Lesson To examine the shape of graphs and how these shapes are determined by differentiation. © Annie Patton Next Slide

Slope of a tangent at a maximum point y Opposite is the graph y=(x−3)(x−2)(x+1). Notice it has a maximum point at x=0. 10 X=0 5 Watch the green line which is the tangent at x=0, its maximum point. x -2 -1 1 2 3 4 5 6 © Annie Patton Next Slide

Slope of a tangent at a minimum point Notice the graph opposite. y=(x−3)(x−2)(x+1). Notice it has a minimum point at x= -1. y Watch the green line which is the tangent at y= -1, its minimum point. 10 5 x -2 -1 1 2 3 4 5 6 y=-1 © Annie Patton Next Slide

Slope of tangent at a Maximum point What we said previously is true for all maximum points. © Annie Patton Next Slide

Slope of tangent at a Minimum point What we said previously is true for all minimum points. © Annie Patton Next Slide

To decide if the turning point is a maximum point 6 y 5 4 3 2 1 x -6 -4 -2 2 4 6 -1 © Annie Patton Next Slide

To decide if the turning point is a minimum point 6 y 5 4 3 2 1 x -6 -4 -2 2 4 6 -1 -2 -3 © Annie Patton Next Slide

Note maximum and minimum points are known as turning points. © Annie Patton Next Slide

Point of Inflection A point of inflection of a curve, is where the direction of the curve changes, but it is not a maximum or minimum point. © Annie Patton Next Slide

Start clicking when you want to see the answer. © Annie Patton Next Slide

Start clicking when you want to see the answer. © Annie Patton Next Slide

Next Slide Start clicking when you want to see the answer. Leaving certificate 2002 Higher Level Paper 1 no 6(c) © Annie Patton Next Slide

Start clicking when you want to see the answer. © Annie Patton Next Slide

Answer the following: © Annie Patton Next Slide

Conclusion © Annie Patton