1. Graphs 10 y 5 x -6 -4 -2 2 4 6
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2. Aim of Lesson
To examine the shape of graphs and how these shapes are determined by differentiation.
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3. Slope of a tangent at a maximum pointy
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
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4. 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
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5. Slope of tangent at a Maximum point
What we said previously is true for all maximum points.
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6. Slope of tangent at a Minimum point
What we said previously is true for all minimum points.
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7. To decide if the turning point is a maximum point6 y 5 4 3 2 1 x -6 -4 -2 2 4 6 -1
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8. To decide if the turning point is a minimum point6 y 5 4 3 2 1 x -6 -4 -2 2 4 6 -1 -2 -3
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9. Note maximum and minimum points are known as turning points.
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10. 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.
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11. Start clicking when you want to see the answer.
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12. Start clicking when you want to see the answer.
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13. Next Slide Start clicking when you want to see the answer.
Leaving certificate 2002 Higher Level Paper 1 no 6(c)
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14. Start clicking when you want to see the answer.
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15. Answer the following:
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16. Conclusion
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